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pairs of shoes hanging on a washing line
James spent two-thirds of a quarter of his wages on some new shoes.

Fractions 3 (Easy)

Fractions are everywhere in life, from sharing cake to measuring land. This 11 Plus Maths quiz helps you explore how parts combine to make a whole.

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Fascinating Fact:

One third of the world’s land is used for farming, meaning humans really do take a large slice of the planet’s pie.

In 11 Plus Maths, pupils learn to understand fractions as equal parts of a whole. This includes comparing, simplifying, and linking them to decimals and percentages.

  • Fraction: A way of showing part of a whole using a numerator and a denominator.
  • Equivalent Fractions: Fractions that represent the same value, such as ½ and 2?4.
  • Simplify: To reduce a fraction to its lowest form without changing its value.
What is an equivalent fraction?

An equivalent fraction has the same value as another fraction, even if the numbers look different. For example, ½ equals 2?4.

How do I simplify a fraction?

Divide both the numerator and the denominator by their highest common factor until you cannot simplify further.

Why are fractions important in maths?

Fractions help us measure, divide, and understand relationships between quantities in real-life situations such as cooking or building.

1 .
What is 3616 as a mixed fraction?
214
213
212
2
36 ÷ 16 = 2.25
2 .
If, in an election, 14 of people voted for the Red Party, 610 voted for the Yellow Party and the rest voted for the Blue Party, what fraction of voters voted for the Blue Party?
310
320
14
1720
First, convert all fractions to the same denominator: 1?4 + 6?10 = 5?20 + 12?20 = 17?20.
20?20 - 17?20 = 3?20
3 .
What is the improper fraction 268 as a mixed fraction?
338
312
314
316
To convert an improper fraction to a mixed fraction, follow these steps:
1. Divide the numerator by the denominator.
2. Note the whole number remainder.
3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original denominator.
STEP 1: 26 ÷ 8 = 3. STEP 2: Remainder 2. STEP 3: 32?8 which can be simplified to 31?4
4 .
James spent two-thirds of a quarter of his wages on some new shoes. If his wages were £312, how much did James’ new shoes cost?
£208
£26
£78
£52
1?4 × £312 = (312 ÷ 4) = £78. That’s a quarter of James’ wages.
78 ÷ 3 = £26. That’s a third of a quarter of James’ wages.
26 x 2 = £52. That’s two-thirds of a quarter of James’ wages
5 .
What is one twelfth of 132?
11
13
9
7
1?12 × 132 = 132 ÷ 12 = 11
6 .
What is 735 as an improper fraction?
3810
385
365
345
To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number part by the denominator.
2. Add this result to the numerator.
3. Write the fraction with step 2 in the numerator and keep the original denominator.
STEP 1: 5 × 7 = 35. STEP 2: 35 + 3 = 38. STEP 3: 38?5
7 .
What is 4927 as an improper fraction?
139
136
133
132
To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number part by the denominator.
2. Add this result to the numerator.
3. Write the fraction with step 2 in the numerator and keep the original denominator.
STEP 1: 4 × 27 = 108. STEP 2: 108 + 9 = 117. STEP 3: 117?27. This can be simplified to 13?3 by dividing the numerator and denominator by 9
8 .
If you are asked to find 45 of something, what is the best method of doing it?
Multiply by 4 then divide by 5
Divide by 4 then multiply by 5
Multiply by 5 then divide by 4
Divide by 5 then multiply by 4
To find one-fifth of something, you divide it by five. To find four-fifths, multiply one-fifth by four
9 .
Susan got one-seventh of the questions in her maths test wrong. If there were 98 questions in the test, how many did Susan get right?
14
69
76
84
The word 'of' means multiply; therefore one-seventh OF something means multiply by 1?7 BUT multiplying by a seventh is the same as dividing by seven: 98 ÷ 7 = 14.
If Susan got 14 questions wrong then she got 98 - 14 = 84 questions right
10 .
What is 15 of 34?
334
120
39
320
Of, in this case, means multiply. You multiply the numbers in the denominator together, and you multiply the numbers in the numerator together to form a single fraction: 1 x 3 = 3 and 5 x 4 = 20 so 1?5 x 3?4 = 3?20
Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)

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