smc-4608-25-Dividing in a given ratio

Ratio, SM-Bank 040

Paul stacks milk cartons into supermarket refrigerator shelves.

Each shelf is stacked with 6 full cream milk cartons, 4 lite milk cartons and 2 skim milk cartons.

Every hour Paul stacks 240 milk cartons in total.

How many lite milk cartons does he stack every hour? (2 marks)

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$80$

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$\text{Total Cartons per shelf}=6+4+2=12$

$\text{Fraction of lite}=\dfrac{4}{12}=\dfrac{1}{3}$

$\text{Total lite per hour}=\dfrac{1}{3}\times 240=80$

Ratio, SM-Bank 037 MC

Tony is making a fruit cake.

The recipe says he needs 3 cups of sultanas for every 5 cups of flour.

If 2.5 cups of flour are used, how many cups of sultanas are needed?

$0.5\ \text{cups}$
$1.5\ \text{cups}$
$2.5\ \text{cups}$
$4.5\ \text{cups}$

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$B$

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$\text{Strategy 1:}$

$2.5\ \text{ is half of }\ 5\ \text{cups of flour, therefore half of}$

$3\ \text{cups of sultanas is required.}$

$\rightarrow\ 1.5\text{ cups of sultanas needed.}$

$\text{Strategy 2:}$

$\text{Let}\ \ n = \text{cups of sultanas needed}$

$\dfrac{n}{2.5}$	$=\dfrac{3}{5}$
$\therefore \ n$	$=\dfrac{3\times 2.5}{5}$
	$=1.5\ \text{cups}$

$\Rightarrow\ B$

Ratio, SM-Bank 036

Milly is using this cupcake recipe.

How many cups of sugar are needed for 20 cupcakes? (2 marks)

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$3\dfrac{3}{4}\ \text{cups}$

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$\text{From the recipe:}$

$\dfrac{3}{4}\ \text{cups} = 4\ \text{cupcakes}$

$\therefore\ \text{Sugar in 20 cupcakes}$	$=\dfrac{3}{4}\times 5$
	$=\dfrac{15}{4}$
	$=3\dfrac{3}{4}\ \text{cups}$

Ratio, SM-Bank 031

Jordan has 4 times as many blue pencils as black pencils.

Altogether he has 90 pencils.

How many blue pencils does he have? (2 marks)

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$72\ \text{blue pencils}$

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$\text{Method 1}$

$\text{Ratio of blue to black}=4:1$

$\text{Total parts}=4+1=5$

$\text{Fraction blue}=\dfrac{4}{5}$

$\text{Number of blue pencils}=\dfrac{4}{5}\times 90=72$

$\text{Method 2 (Advanced)}$

$\text{Let}\ \ x = \text{the number of black pencils}$

$\text{Then the number of blue pencils}=4x$

$\text{Total pencils }= x + 4x$	$=5x$
$\rightarrow\ 5x$	$= 90$
$x$	$=\dfrac{90}{5}= 18$

$\therefore \ \text{The number of blue pencils}$

$=90-18= 72$

Ratio, SM-Bank 030 MC

A school has 360 students.

The ratio of boys to girls is 4 to 6.

How many boys attend the school?

$90$
$144$
$216$
$240$

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$B$

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$\text{Total students}=4+6=10$

$\text{Fraction of boys}=\dfrac{4}{10}=\dfrac{2}{5}$

$\text{Boys}=\dfrac{2}{5}\times 360=144$

$\Rightarrow B$

Ratio, SM-Bank 028 MC

A little athletics club is established in a town.

In the first week, 5 girls and 6 boys joined the club.

In the second week, another 4 boys and some more girls joined the club.

The number of girls in the club was now double the number of boys.

How many girls joined the club in the second week?

$7$
$15$
$17$
$20$

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$B$

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$\text{1st week}\rightarrow 6\ \text{boys.}$

$\text{2nd week }\rightarrow 6+4 = 10\ \text{boys.}$

$\text{Total girls in 2nd week.}$

$= 2\times 10$

$= 20$

$\therefore\ \text{Girls joining in 2nd week.}$

$= 20-5$

$= 15$

$\Rightarrow B$

Ratio, SM-Bank 027 MC

Muriel made a batch of cookies.

Each cookie had 4 chocolate chips and 3 jelly snakes on it.

Muriel used 39 jelly snakes in the batch of cookies.

How many chocolate chips did she use?

$13$
$26$
$52$
$78$

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$C$

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$\text{Number of cookies made}$

$=\dfrac{39}{3}$

$=13$

$\therefore\ \text{Chocolate chips used}$

$=13\times 4$

$=52$

$\Rightarrow C$

Ratio, SM-Bank 025

The ratio of the angles in a triangle is 1:2:5.

Calculate the sizes of all three angles? (2 marks)

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$22.5^{\circ}, 45^{\circ} \text{ and}\ 112.5^{\circ}$

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$\text{Total parts}=1+2+5=8\ \text{and the angle sum of a triangle}=180^{\circ}$

$\dfrac{1}{8}\times 180$	$=22.5$
$\dfrac{2}{8}\times 180$	$=45$
$\dfrac{5}{8}\times 180$	$=112.5$

$\therefore\ \text{The angles in the triangle are }22.5^{\circ}, 45^{\circ} \text{ and}\ 112.5^{\circ}$

Ratio, SM-Bank 022

Divide $420 in the ratio 1:3:2. (2 marks)

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$$70, $210 \text{ and } $140$

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$\text{Total number of parts}=1+3+2=6$

$\dfrac{1}{6}\times 420$	$=70$
$\dfrac{3}{6}\times 420$	$=210$
$\dfrac{2}{6}\times 420$	$=140$

$\therefore\ $420\ \text{divided in the ratio }\ 1:3:2\ \text{ is }\ $70, $210\ \text{and } $140.$

Ratio, SM-Bank 021

Divide 84 days in the ratio 3:4. (2 marks)

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$36\ \text{days and } 48\ \text{days}$

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$\text{Total number of parts}=3+4=7$

$\dfrac{3}{7}\times 84$	$=36$
$\dfrac{4}{7}\times 84$	$=48$

$\therefore\ 84\ \text{days divided in the ratio }3:4\ \text{is }36\ \text{days and } 48\ \text{days.}$

Ratio, SM-Bank 020

Divide 480 tonnes in the ratio 1:5. (2 marks)

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$80\ \text{tonnes and}\ 400\ \text{tonnes}$

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$\text{Total number of parts}=1+5=6$

$\dfrac{1}{6}\times 480$	$=80$
$\dfrac{5}{6}\times 480$	$=400$

$\therefore\ 480\ \text{tonnes divided in the ratio }1:5\ \text{is }80\ \text{tonnes and } 400\ \text{tonnes.}$

Ratio, SM-Bank 019

Divide $130 in the ratio 5:8. (2 marks)

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$$50\ \text{and}\ $80$

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$\text{Total number of parts}=5+8=13$

$\dfrac{5}{13}\times 130$	$=50$
$\dfrac{8}{13}\times 130$	$=80$

$\therefore\ \$130\ \text{divided in the ratio }5:8\ \text{is }$50\ \text{and}\ $80.$

Ratio, SM-Bank 018

The ratio of kilograms of bananas to apples at the fruit shop is $11:5$.

What fraction of the fruit is bananas? (1 mark)

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If there are 128 kilograms of bananas and apples altogether, how many kilograms of bananas are there? (2 marks)

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a. $\dfrac{11}{16}$

b. $88\ \text{kg of bananas}$

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a. $\text{Total fruits}=11+5=16$

$\text{Fraction bananas}=\dfrac{11}{16}$

b.	$\text{Kilograms of bananas}$	$=\dfrac{11}{16}\times 128$
		$=88$

$\therefore\ \text{There are }88\ \text{kgs of bananas.}$

Ratio, SM-Bank 017

The ratio of dogs to cats in an animal rescue shelter is $5:4$.

What fraction of the animals are dogs? (1 mark)

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What fraction of the animals are cats? (1 mark)

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If there are 36 animals in the shelter, how many are dogs? (2 marks)

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a. $\dfrac{5}{9}$

b. $\dfrac{4}{9}$

c. $20\ \text{dogs}$

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a. $\text{Total animals}=5+4=9$

$\text{Fraction dogs}=\dfrac{5}{9}$

b. $\text{Fraction cats}=\dfrac{4}{9}$

c.	$\text{Number of dogs}$	$=\dfrac{5}{9}\times 36$
		$=20$

$\therefore\ \text{There are }20\ \text{dogs in the shelter.}$

\(\dfrac{n}{2.5}\)	\(=\dfrac{3}{5}\)
\(\therefore \ n\)	\(=\dfrac{3\times 2.5}{5}\)
	\(=1.5\ \text{cups}\)

\(\therefore\ \text{Sugar in 20 cupcakes}\)	\(=\dfrac{3}{4}\times 5\)
	\(=\dfrac{15}{4}\)
	\(=3\dfrac{3}{4}\ \text{cups}\)

\(\text{Total pencils }= x + 4x\)	\(=5x\)
\(\rightarrow\ 5x\)	\(= 90\)
\(x\)	\(=\dfrac{90}{5}= 18\)

\(\dfrac{1}{8}\times 180\)	\(=22.5\)
\(\dfrac{2}{8}\times 180\)	\(=45\)
\(\dfrac{5}{8}\times 180\)	\(=112.5\)

\(\dfrac{1}{6}\times 420\)	\(=70\)
\(\dfrac{3}{6}\times 420\)	\(=210\)
\(\dfrac{2}{6}\times 420\)	\(=140\)

\(\dfrac{3}{7}\times 84\)	\(=36\)
\(\dfrac{4}{7}\times 84\)	\(=48\)

\(\dfrac{1}{6}\times 480\)	\(=80\)
\(\dfrac{5}{6}\times 480\)	\(=400\)

\(\dfrac{5}{13}\times 130\)	\(=50\)
\(\dfrac{8}{13}\times 130\)	\(=80\)

b.	\(\text{Kilograms of bananas}\)	\(=\dfrac{11}{16}\times 128\)
		\(=88\)