Mastery Guide: Metric Conversions, Multi-Unit Arithmetic & 24-Hour Time Calculations

a) $34\text{ km}$ into $\text{m}$:
$$1\text{ km} = 1,000\text{ m} \implies 34 \times 1,000 = \mathbf{34,000\text{ m}}$$

b) $930\text{ m } 74\text{ km}$ into $\text{m}$:
$$74\text{ km } 930\text{ m} = (74 \times 1,000) + 930 = 74,000 + 930 = \mathbf{74,930\text{ m}}$$

c) $970\text{ m}$ into $\text{km}$:
$$1,000\text{ m} = 1\text{ km} \implies 970 \div 1,000 = \mathbf{0.97\text{ km}}\quad \left(\text{or }\frac{97}{100}\text{ km}\right)$$

d) $5,890\text{ m}$ into $\text{km}$ and $\text{m}$:
$$5,890 \div 1,000 = 5\text{ R } 890 \implies \mathbf{5\text{ km } 890\text{ m}}$$

e) $67\text{ m}$ into $\text{cm}$:
$$1\text{ m} = 100\text{ cm} \implies 67 \times 100 = \mathbf{6,700\text{ cm}}$$

f) $650\text{ m } 46\text{ cm}$ into $\text{cm}$:
$$(650 \times 100) + 46 = 65,000 + 46 = \mathbf{65,046\text{ cm}}$$

g) $840\text{ cm}$ into $\text{m}$:
$$840 \div 100 = \mathbf{8.4\text{ m}}\quad (\text{or } 8\text{ m } 40\text{ cm})$$

h) $107\text{ cm}$ into $\text{mm}$:
$$1\text{ cm} = 10\text{ mm} \implies 107 \times 10 = \mathbf{1,070\text{ mm}}$$

i) $6\text{ m } 99\text{ cm}$ into $\text{mm}$:
$$6\text{ m } 99\text{ cm} = (6 \times 100 + 99)\text{ cm} = 699\text{ cm} \implies 699 \times 10 = \mathbf{6,990\text{ mm}}$$

j) $70\text{ mm}$ into $\text{cm}$:
$$70 \div 10 = \mathbf{7\text{ cm}}$$

k) $485\text{ mm}$ into $\text{cm}$ and $\text{mm}$:
$$485 \div 10 = 48\text{ R } 5 \implies \mathbf{48\text{ cm } 5\text{ mm}}$$

l) $900\text{ m}$ into $\text{cm}$:
$$900 \times 100 = \mathbf{90,000\text{ cm}}$$

Given:
Green cloth $= 4\text{ m } 35\text{ cm} = (4 \times 100) + 35 = 435\text{ cm}$
White cloth $= 6\text{ m } 79\text{ cm} = (6 \times 100) + 79 = 679\text{ cm}$

Total cloth in centimetres:
$$435\text{ cm} + 679\text{ cm} = \mathbf{1,114\text{ cm}}\quad (= 11\text{ m } 14\text{ cm})$$

$$1\text{ cm} = 10\text{ mm} \implies 140 \times 10 = \mathbf{1,400\text{ mm}}$$

a) Difference:
$$80\text{ cm } 6\text{ mm} - 17\text{ cm } 9\text{ mm}$$ Borrow $1\text{ cm} = 10\text{ mm} \implies 79\text{ cm } 16\text{ mm} - 17\text{ cm } 9\text{ mm} = \mathbf{62\text{ cm } 7\text{ mm}}$$

b) Total length in millimetres:
Rope 1 $= (17 \times 10) + 9 = 179\text{ mm}$
Rope 2 $= (80 \times 10) + 6 = 806\text{ mm}$
$$\text{Total} = 179 + 806 = \mathbf{985\text{ mm}}$$

$$\begin{array}{rcc} & \text{m} & \text{cm} \\ & 276 & 20 \\ + & 689 & 98 \\ \hline & 965 & 118 \end{array}$$ Since $118\text{ cm} = 1\text{ m } 18\text{ cm}$, carry $1\text{ m}$ to metres:
$$\text{Total length} = \mathbf{966\text{ m } 18\text{ cm}}$$

Comparing $4\text{ km } 196\text{ m}$ and $5\text{ km } 298\text{ m}$, Ahmer's house is nearer.

Difference:
$$5\text{ km } 298\text{ m} - 4\text{ km } 196\text{ m} = \mathbf{1\text{ km } 102\text{ m}}\quad (= 1,102\text{ m})$$

Fiza's park $= (2 \times 1,000) + 117 = 2,117\text{ m}$
Maheen's park $= (3 \times 1,000) + 214 = 3,214\text{ m}$
$$\text{Difference} = 3,214\text{ m} - 2,117\text{ m} = \mathbf{1,097\text{ m}}\quad (= 1\text{ km } 97\text{ m})$$

(a) $22\text{ kg}$ into $\text{g}$: $22 \times 1,000 = \mathbf{22,000\text{ g}}$

(b) $10\text{ kg } 20\text{ g}$ into $\text{gram}$: $(10 \times 1,000) + 20 = 10,000 + 20 = \mathbf{10,020\text{ g}}$

(c) $5\text{ kg } 850\text{ g}$ into $\text{g}$: $(5 \times 1,000) + 850 = 5,000 + 850 = \mathbf{5,850\text{ g}}$

(d) $4.50\text{ kg}$ into $\text{g}$: $4.50 \times 1,000 = \mathbf{4,500\text{ g}}$

(e) $20.5\text{ kg } 100\text{ g}$ into $\text{gram}$: $(20.5 \times 1,000) + 100 = 20,500 + 100 = \mathbf{20,600\text{ g}}$

(f) $75\text{ kg } 680\text{ g}$ into $\text{g}$: $(75 \times 1,000) + 680 = 75,000 + 680 = \mathbf{75,680\text{ g}}$

(g) $1,500\text{ g}$ into $\text{kg}$: $1,500 \div 1,000 = \mathbf{1.5\text{ kg}}\quad (1\text{ kg } 500\text{ g})$

(h) $20\text{ kg } 200\text{ g}$ into $\text{kg}$: $20 + (200 \div 1,000) = 20 + 0.2 = \mathbf{20.2\text{ kg}}$

(i) $850\text{ g}$ into $\text{kg}$: $850 \div 1,000 = \mathbf{0.85\text{ kg}}$

(j) $25\text{ g}$ into $\text{kg}$: $25 \div 1,000 = \mathbf{0.025\text{ kg}}$

(k) $3,500\text{ g}$ into $\text{kg}$: $3,500 \div 1,000 = \mathbf{3.5\text{ kg}}\quad (3\text{ kg } 500\text{ g})$

(l) $95,500\text{ g}$ into $\text{kg}$: $95,500 \div 1,000 = \mathbf{95.5\text{ kg}}$

$$\text{Total sugar} = 50\text{ kg} + 30\text{ kg} = 80\text{ kg}$$ $$\text{In grams} = 80 \times 1,000 = \mathbf{80,000\text{ g}}$$

$$\begin{array}{rcc} & \text{kg} & \text{g} \\ & 85 & 500 \\ - & 45 & 350 \\ \hline & \mathbf{40} & \mathbf{150} \end{array}$$ $$\text{Rice left} = \mathbf{40\text{ kg } 150\text{ g}}$$

$$\text{Total weight} = 44\text{ kg} + 35\text{ kg} = 79\text{ kg}$$ $$\text{In grams} = 79 \times 1,000 = \mathbf{79,000\text{ g}}$$

$$\begin{array}{rcc} & \text{kg} & \text{g} \\ & 300 & 890 \\ - & 250 & 675 \\ \hline & \mathbf{50} & \mathbf{215} \end{array}$$ $$\text{Difference} = \mathbf{50\text{ kg } 215\text{ g}}$$

(i) Total weight:
$$32\text{ kg } 350\text{ g} + 30\text{ kg } 200\text{ g} = \mathbf{62\text{ kg } 550\text{ g}}$$

(ii) Difference:
$$32\text{ kg } 350\text{ g} - 30\text{ kg } 200\text{ g} = \mathbf{2\text{ kg } 150\text{ g}}$$

$$\text{Weight gained} = 14\text{ kg } 800\text{ g} - 10\text{ kg } 300\text{ g} = \mathbf{4\text{ kg } 500\text{ g}}$$

Total weight in grams $= 2.5 \times 1,000 = 2,500\text{ g}$
Candies weight in grams $= (1 \times 1,000) + 400 = 1,400\text{ g}$
$$\text{Weight of chocolates} = 2,500\text{ g} - 1,400\text{ g} = \mathbf{1,100\text{ g}}\quad (= 1.1\text{ kg})$$

(a) $15\text{ l}$ into $\text{ml}$: $15 \times 1,000 = \mathbf{15,000\text{ ml}}$

(b) $30\text{ l } 500\text{ ml}$ into $\text{ml}$: $(30 \times 1,000) + 500 = \mathbf{30,500\text{ ml}}$

(c) $4\text{ l } 60\text{ ml}$ into $\text{ml}$: $(4 \times 1,000) + 60 = \mathbf{4,060\text{ ml}}$

(d) $2.5\text{ l}$ into $\text{ml}$: $2.5 \times 1,000 = \mathbf{2,500\text{ ml}}$

(e) $40.5\text{ l } 300\text{ ml}$ into $\text{ml}$: $(40.5 \times 1,000) + 300 = 40,500 + 300 = \mathbf{40,800\text{ ml}}$

(f) $36\text{ l } 480\text{ ml}$ into $\text{ml}$: $(36 \times 1,000) + 480 = \mathbf{36,480\text{ ml}}$

(g) $2,400\text{ ml}$ into $\text{l}$: $2,400 \div 1,000 = \mathbf{2.4\text{ l}}\quad (2\text{ l } 400\text{ ml})$

(h) $80\text{ l } 940\text{ ml}$ into $\text{l}$: $80 + (940 \div 1,000) = \mathbf{80.94\text{ l}}$

(i) $40.5\text{ l } 850\text{ ml}$ into $\text{l}$: $40.5 + 0.85 = \mathbf{41.35\text{ l}}$

(j) $28\text{ ml}$ into $\text{l}$: $28 \div 1,000 = \mathbf{0.028\text{ l}}$

(k) $4,000\text{ ml}$ into $\text{l}$: $4,000 \div 1,000 = \mathbf{4\text{ l}}$

(l) $95,500\text{ ml}$ into $\text{l}$: $95,500 \div 1,000 = \mathbf{95.5\text{ l}}$

(i) $33\text{ l } 560\text{ ml} + 41\text{ l } 430\text{ ml}$:
$$33\text{ l } 560\text{ ml} + 41\text{ l } 430\text{ ml} = 74\text{ l } 990\text{ ml} = \mathbf{74\text{ l } 990\text{ ml}}$$

(ii) $120\text{ l } 305\text{ ml} + 206\text{ l } 540\text{ ml}$:
$$\mathbf{326\text{ l } 845\text{ ml}}$$

(iii) $18\text{ l } 239\text{ ml} + 24\text{ l } 179\text{ ml} + 26\text{ l } 100\text{ ml}$:
$$\text{ml} = 239 + 179 + 100 = 518\text{ ml},\quad \text{l} = 18 + 24 + 26 = 68\text{ l} \implies \mathbf{68\text{ l } 518\text{ ml}}$$

(iv) $62\text{ l } 409\text{ ml} + 43\text{ l } 498\text{ ml}$:
$$\mathbf{105\text{ l } 907\text{ ml}}$$

(v) $31\text{ l } 177\text{ ml} + 55\text{ l } 321\text{ ml} + 84\text{ l } 235\text{ ml}$:
$$\text{ml} = 177 + 321 + 235 = 733\text{ ml},\quad \text{l} = 31 + 55 + 84 = 170\text{ l} \implies \mathbf{170\text{ l } 733\text{ ml}}$$

(vi) $33\text{ l } 460\text{ ml} + 66\text{ l } 830\text{ ml}$:
$$\text{ml} = 460 + 830 = 1,290\text{ ml} = 1\text{ l } 290\text{ ml},\quad \text{l} = 33 + 66 + 1 = 100\text{ l} \implies \mathbf{100\text{ l } 290\text{ ml}}$$

(i) $73\text{ l } 430\text{ ml} - 29\text{ l } 200\text{ ml}$: $\mathbf{44\text{ l } 230\text{ ml}}$

(ii) $290\text{ l } 444\text{ ml} - 98\text{ l } 237\text{ ml}$: $\mathbf{192\text{ l } 207\text{ ml}}$

(iii) $545\text{ l } 150\text{ ml} - 183\text{ l } 125\text{ ml}$: $\mathbf{362\text{ l } 25\text{ ml}}$

(iv) $744\text{ l } 493\text{ ml} - 489\text{ l } 243\text{ ml}$: $\mathbf{255\text{ l } 250\text{ ml}}$

(v) $204\text{ l } 200\text{ ml} - 201\text{ l } 150\text{ ml}$: $\mathbf{3\text{ l } 50\text{ ml}}$

(vi) $843\text{ l } 421\text{ ml} - 507\text{ l } 358\text{ ml}$: $\mathbf{336\text{ l } 63\text{ ml}}$

$$\text{Total water} = 16.4 + 9.9 = \mathbf{26.3\text{ litres}}$$

$$\text{Total oil} = 3.5\text{ l} + 4.6\text{ l} = 8.1\text{ l}$$ $$\text{In millilitres} = 8.1 \times 1,000 = \mathbf{8,100\text{ ml}}$$

$$3\text{ l } 450\text{ ml} + 260\text{ ml} = \mathbf{3\text{ l } 710\text{ ml}}\quad (= 3,710\text{ ml})$$

$$\begin{array}{rcc} & \text{l} & \text{ml} \\ & 800 & 490 \\ + & 600 & 370 \\ \hline & \mathbf{1,400} & \mathbf{860} \end{array}$$ $$\text{Total petrol sold} = \mathbf{1,400\text{ l } 860\text{ ml}}$$

$$\text{Remaining petrol} = 30 - 18 = 12\text{ liters}$$ $$\text{In millilitres} = 12 \times 1,000 = \mathbf{12,000\text{ ml}}$$

$$\text{Water left} = 1,250 - 870 = \mathbf{380\text{ liters}}$$

$$\text{Remaining stock} = 232 - 117 = \mathbf{115\text{ liters}}$$

The first tank has more water.

$$\text{Difference} = 560 - 433 = \mathbf{127\text{ liters}}$$

a) $45\text{ h}$ to $\text{min}$: $45 \times 60 = \mathbf{2,700\text{ min}}$

b) $240\text{ h } 56\text{ min}$ to $\text{min}$: $(240 \times 60) + 56 = 14,400 + 56 = \mathbf{14,456\text{ min}}$

c) $960\text{ min}$ to $\text{h}$: $960 \div 60 = \mathbf{16\text{ h}}$

d) $440\text{ min}$ to $\text{h}$ and $\text{min}$: $440 \div 60 = 7\text{ R } 20 \implies \mathbf{7\text{ h } 20\text{ min}}$

e) $64\text{ min}$ to $\text{sec}$: $64 \times 60 = \mathbf{3,840\text{ sec}}$

f) $180\text{ min}$ to $\text{sec}$: $180 \times 60 = \mathbf{10,800\text{ sec}}$

g) $544\text{ sec}$ to $\text{min}$ and $\text{sec}$: $544 \div 60 = 9\text{ R } 4 \implies \mathbf{9\text{ min } 4\text{ sec}}$

h) $600\text{ sec}$ to $\text{min}$: $600 \div 60 = \mathbf{10\text{ min}}$

a) $56\text{ years}$ into $\text{months}$: $56 \times 12 = \mathbf{672\text{ months}}$

b) $34\text{ years } 10\text{ months}$ into $\text{months}$: $(34 \times 12) + 10 = 408 + 10 = \mathbf{418\text{ months}}$

c) $48\text{ months}$ into $\text{years}$: $48 \div 12 = \mathbf{4\text{ years}}$

d) $56\text{ months}$ into $\text{years}$ and $\text{months}$: $56 \div 12 = 4\text{ R } 8 \implies \mathbf{4\text{ years } 8\text{ months}}$

e) $78\text{ weeks}$ into $\text{days}$: $78 \times 7 = \mathbf{546\text{ days}}$

f) $12\text{ weeks } 6\text{ days}$ into $\text{days}$: $(12 \times 7) + 6 = 84 + 6 = \mathbf{90\text{ days}}$

g) $49\text{ days}$ into $\text{weeks}$: $49 \div 7 = \mathbf{7\text{ weeks}}$

h) $180\text{ days}$ into $\text{months}$: $180 \div 30 = \mathbf{6\text{ months}}$

i) $67\text{ months}$ into $\text{days}$: $67 \times 30 = \mathbf{2,010\text{ days}}$

j) $44\text{ months } 29\text{ days}$ into $\text{days}$: $(44 \times 30) + 29 = 1,320 + 29 = \mathbf{1,349\text{ days}}$

a) $3\text{ h } 20\text{ min} + 5\text{ h } 43\text{ min}$:
$$\text{min} = 20 + 43 = 63\text{ min} = 1\text{ h } 3\text{ min},\quad \text{h} = 3 + 5 + 1 = 9\text{ h} \implies \mathbf{9\text{ h } 3\text{ min}}$$

b) $13\text{ min } 12\text{ sec} + 15\text{ min } 19\text{ sec}$:
$$\mathbf{28\text{ min } 31\text{ sec}}$$

c) $33\text{ years } 8\text{ months} + 40\text{ years } 11\text{ months}$:
$$\text{months} = 8 + 11 = 19\text{ months} = 1\text{ yr } 7\text{ mo},\quad \text{yr} = 33 + 40 + 1 = 74\text{ yr} \implies \mathbf{74\text{ years } 7\text{ months}}$$

d) $2\text{ weeks } 3\text{ days} + 8\text{ weeks } 1\text{ day}$:
$$\mathbf{10\text{ weeks } 4\text{ days}}$$

e) $117\text{ months} + 7\text{ months}$:
$$124\text{ months} = 124 \div 12 = \mathbf{10\text{ years } 4\text{ months}}\quad (\text{or } 124\text{ months})$$

f) $8\text{ months } 12\text{ days} + 2\text{ months } 14\text{ days}$:
$$\mathbf{10\text{ months } 26\text{ days}}$$

a) $16\text{ h } 49\text{ min} - 3\text{ h } 53\text{ min}$:
Borrow $1\text{ h} = 60\text{ min} \implies 15\text{ h } 109\text{ min} - 3\text{ h } 53\text{ min} = \mathbf{12\text{ h } 56\text{ min}}$$

b) $44\text{ min } 44\text{ sec} - 36\text{ min } 16\text{ sec}$:
$$\mathbf{8\text{ min } 28\text{ sec}}$$

c) $8\text{ weeks } 1\text{ day} - 2\text{ weeks } 3\text{ days}$:
Borrow $1\text{ week} = 7\text{ days} \implies 7\text{ weeks } 8\text{ days} - 2\text{ weeks } 3\text{ days} = \mathbf{5\text{ weeks } 5\text{ days}}$$

d) $17\text{ months} - 10\text{ months } 12\text{ days}$:
Borrow $1\text{ month} = 30\text{ days} \implies 16\text{ months } 30\text{ days} - 10\text{ months } 12\text{ days} = \mathbf{6\text{ months } 18\text{ days}}$$

e) $40\text{ months } 28\text{ days} - 38\text{ months } 17\text{ days}$:
$$\mathbf{2\text{ months } 11\text{ days}}$$

$$\begin{array}{rcc} & \text{h} & \text{min} \\ & 5 & 56 \\ + & 6 & 22 \\ \hline & 11 & 78 \end{array}$$ Since $78\text{ min} = 1\text{ h } 18\text{ min}$:
$$\text{Total time} = \mathbf{12\text{ hours } 18\text{ minutes}}$$

The English project takes more time.

$$\text{Difference} = 2\text{ weeks } 5\text{ days} - 1\text{ week } 6\text{ days}$$ Borrow $1\text{ week} = 7\text{ days} \implies 1\text{ week } 12\text{ days} - 1\text{ week } 6\text{ days} = \mathbf{6\text{ days}}$$

$$\text{Difference} = 11\text{ years } 8\text{ months} - 10\text{ years } 5\text{ months} = 1\text{ year } 3\text{ months}$$ $$\text{In months} = (1 \times 12) + 3 = \mathbf{15\text{ months}}$$

a) Total time in minutes:
$$3\text{ h } 12\text{ min} + 1\text{ h } 50\text{ min} = 4\text{ h } 62\text{ min} = 5\text{ h } 2\text{ min}$$ $$\text{In minutes} = (5 \times 60) + 2 = \mathbf{302\text{ minutes}}$$

b) More time spent on:
Umer spends more time on Maths homework.
$$\text{Difference} = 3\text{ h } 12\text{ min} - 1\text{ h } 50\text{ min} = 2\text{ h } 72\text{ min} - 1\text{ h } 50\text{ min} = \mathbf{1\text{ hour } 22\text{ minutes}}\quad (82\text{ min})$$

a) There are ______ metres in 2 kilometres.
(i) 500   (ii) 1,000   (iii) 200   (iv) 2,000 ✓
Explanation: $2 \times 1,000 = 2,000\text{ m}$.

b) To measure ______ hours, minutes and seconds are used.
(i) time ✓   (ii) distance   (iii) area   (iv) length
Explanation: Hours, minutes, and seconds quantify time durations.

c) There are ______ months in $\frac{1}{2}$ year.
(i) 6 ✓   (ii) 12   (iii) 9   (iv) 5
Explanation: $\frac{1}{2} \times 12 = 6\text{ months}$.

d) There are ______ days in 10 months.
(i) 300 ✓   (ii) 30   (iii) 15   (iv) 45
Explanation: $10 \times 30 = 300\text{ days}$.

e) There are ______ minutes in 5 hours.
(i) 60   (ii) 300 ✓   (iii) 200   (iv) 50
Explanation: $5 \times 60 = 300\text{ minutes}$.

f) There are ______ days in 7 weeks.
(i) 49 ✓   (ii) 42   (iii) 7   (iv) 14
Explanation: $7 \times 7 = 49\text{ days}$.

g) $3.5\text{ kg} = $ ______
(i) 350 g   (ii) 3,500 g ✓   (iii) 35 g   (iv) 35,000 g
Explanation: $3.5 \times 1,000 = 3,500\text{ g}$.

h) $560\text{ ml} = $ ______
(i) 56 l   (ii) 5.6 l   (iii) 0.56 l ✓   (iv) 0.056 l
Explanation: $560 \div 1,000 = 0.56\text{ l}$.

a) $52\text{ km}$ to $\text{m}$: $52 \times 1,000 = \mathbf{52,000\text{ m}}$

b) $21\text{ km } 103\text{ metres}$ to $\text{m}$: $(21 \times 1,000) + 103 = \mathbf{21,103\text{ m}}$

c) $1,050\text{ m}$ to $\text{km}$: $1,050 \div 1,000 = \mathbf{1.05\text{ km}}\quad (1\text{ km } 50\text{ m})$

d) $6,000\text{ m}$ to $\text{km}$ and $\text{m}$: $6,000 \div 1,000 = \mathbf{6\text{ km } 0\text{ m}}\quad (6\text{ km})$

e) $198\text{ m}$ to $\text{cm}$: $198 \times 100 = \mathbf{19,800\text{ cm}}$

f) $500\text{ m } 66\text{ cm}$ into $\text{cm}$: $(500 \times 100) + 66 = \mathbf{50,066\text{ cm}}$

g) $640\text{ cm}$ into $\text{m}$ and $\text{cm}$: $640 \div 100 = \mathbf{6\text{ m } 40\text{ cm}}$

h) $98\text{ cm}$ into $\text{mm}$: $98 \times 10 = \mathbf{980\text{ mm}}$

a) $22\text{ h } 6\text{ min}$ to $\text{min}$: $(22 \times 60) + 6 = 1,320 + 6 = \mathbf{1,326\text{ min}}$

b) $360\text{ min}$ to $\text{h}$: $360 \div 60 = \mathbf{6\text{ h}}$

c) $580\text{ min}$ into $\text{h}$ and $\text{min}$: $580 \div 60 = 9\text{ R } 40 \implies \mathbf{9\text{ h } 40\text{ min}}$

d) $64\text{ min}$ into $\text{sec}$: $64 \times 60 = \mathbf{3,840\text{ sec}}$

e) $795\text{ sec}$ into $\text{min}$ and $\text{sec}$: $795 \div 60 = 13\text{ R } 15 \implies \mathbf{13\text{ min } 15\text{ sec}}$

f) $198\text{ sec}$ into $\text{min}$: $198 \div 60 = \mathbf{3.3\text{ min}}\quad (3\text{ min } 18\text{ sec})$

a) $78\text{ years}$ into $\text{months}$: $78 \times 12 = \mathbf{936\text{ months}}$

b) $14\text{ years } 6\text{ months}$ into $\text{months}$: $(14 \times 12) + 6 = 168 + 6 = \mathbf{174\text{ months}}$

c) $26\text{ months}$ to $\text{years}$ and $\text{months}$: $26 \div 12 = 2\text{ R } 2 \implies \mathbf{2\text{ years } 2\text{ months}}$

d) $9\text{ weeks } 2\text{ days}$ into $\text{days}$: $(9 \times 7) + 2 = 63 + 2 = \mathbf{65\text{ days}}$

e) $35\text{ days}$ into $\text{weeks}$: $35 \div 7 = \mathbf{5\text{ weeks}}$

f) $420\text{ days}$ into $\text{months}$: $420 \div 30 = \mathbf{14\text{ months}}$

a) $6\text{ h } 52\text{ min} + 9\text{ h } 12\text{ min}$:
$$\text{min} = 52 + 12 = 64\text{ min} = 1\text{ h } 4\text{ min},\quad \text{h} = 6 + 9 + 1 = 16\text{ h} \implies \mathbf{16\text{ h } 4\text{ min}}$$

b) $46\text{ min } 46\text{ sec} + 11\text{ min } 10\text{ sec}$:
$$\mathbf{57\text{ min } 56\text{ sec}}$$

c) $66\text{ years } 9\text{ months} + 22\text{ years } 7\text{ months}$:
$$\text{mo} = 9 + 7 = 16 = 1\text{ yr } 4\text{ mo},\quad \text{yr} = 66 + 22 + 1 = 89\text{ yr} \implies \mathbf{89\text{ years } 4\text{ months}}$$

d) $34\text{ min } 20\text{ sec} - 12\text{ min } 55\text{ sec}$:
Borrow $1\text{ min} = 60\text{ sec} \implies 33\text{ min } 80\text{ sec} - 12\text{ min } 55\text{ sec} = \mathbf{21\text{ min } 25\text{ sec}}$$

e) $6\text{ weeks } 5\text{ days} + 11\text{ weeks } 5\text{ days}$:
$$\text{days} = 5 + 5 = 10 = 1\text{ wk } 3\text{ days},\quad \text{wk} = 6 + 11 + 1 = 18\text{ wk} \implies \mathbf{18\text{ weeks } 3\text{ days}}$$

f) $49\text{ months } 19\text{ days} + 55\text{ months}$:
$$\mathbf{104\text{ months } 19\text{ days}}\quad (= 8\text{ years } 8\text{ months } 19\text{ days})$$

a) Total length:
$$15\text{ m } 13\text{ cm} + 12\text{ m } 42\text{ cm} = \mathbf{27\text{ m } 55\text{ cm}}$$

b) Difference:
$$15\text{ m } 13\text{ cm} - 12\text{ m } 42\text{ cm}$$ Borrow $1\text{ m} = 100\text{ cm} \implies 14\text{ m } 113\text{ cm} - 12\text{ m } 42\text{ cm} = \mathbf{2\text{ m } 71\text{ cm}}$$

a) Shirt taking more time:
The tailor takes more time for Shirt A.
$$\text{Difference} = 3\text{ h } 45\text{ min} - 2\text{ h } 21\text{ min} = \mathbf{1\text{ hour } 24\text{ minutes}}$$

b) Total time for both shirts:
$$3\text{ h } 45\text{ min} + 2\text{ h } 21\text{ min} = 5\text{ h } 66\text{ min} = \mathbf{6\text{ hours } 6\text{ minutes}}$$