1.16 Equivalent fractions, simplifying and ordering fractions
9 exam questions worth 19 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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Which fraction is equivalent to \frac{3}{5}?
Choose one answer.
Correct Not quite: the answer is \( \frac{9}{15} \)
Mark scheme
B: \frac{9}{15}
Model answer
\frac{9}{15} (B). Multiply top and bottom by 3.
Simplify \dfrac{36}{48}.
Mark scheme
M1: divides top and bottom by a common factor (e.g. 12, 6, 4 or 2); A1: 3/4
Model answer
The HCF of 36 and 48 is 12, so 36/48 = 3/4.
(a) Write \frac{17}{5} as a mixed number. (b) Write 4\frac{3}{8} as an improper fraction.
Mark scheme
B1: 3 2/5; B1: 35/8
Model answer
(a) 17 ÷ 5 = 3 remainder 2, so 3 2/5. (b) 4 × 8 + 3 = 35, so 35/8.
Write these fractions in order of size, smallest first. \frac{3}{4} \frac{2}{3} \frac{5}{8}
Mark scheme
M1: common denominator 24 (or decimals); A1: 18/24, 16/24, 15/24 (or 0.75, 0.667, 0.625); A1: 5/8, 2/3, 3/4
Model answer
With denominator 24: 3/4 = 18/24, 2/3 = 16/24, 5/8 = 15/24. Smallest first: 5/8, 2/3, 3/4.
Which is greater, \frac{7}{9} or \frac{5}{7}? Show your working.
Mark scheme
M1: common denominator 63 (49/63 and 45/63) or decimals (0.778 and 0.714); A1: 7/9
Model answer
7/9 = 49/63 and 5/7 = 45/63. Since 49 > 45, 7/9 is greater.
Find the missing numbers. \dfrac{5}{8} = \dfrac{?}{24} = \dfrac{35}{?}
Mark scheme
B1: 15; B1: 56
Model answer
8 × 3 = 24, so 5 × 3 = 15. 5 × 7 = 35, so 8 × 7 = 56.
Write these in order of size, smallest first. -\frac{1}{2} -\frac{2}{3} -\frac{3}{8}
Mark scheme
M1: converts to a common denominator or decimals; A1: correct values (e.g. -12/24, -16/24, -9/24); A1: -2/3, -1/2, -3/8
Model answer
As decimals: -0.5, -0.667, -0.375. The smallest is the most negative: -2/3, -1/2, -3/8.
In a class of 30 students, 18 walk to school. What fraction of the class walk to school? Give your answer in its simplest form.
Mark scheme
M1: 18/30; A1: 3/5
Model answer
18/30 = 3/5 (dividing top and bottom by 6).
Amir says, '\frac{3}{8} is greater than \frac{1}{2} because 8 is greater than 2.' Is Amir correct? You must show your working.
Mark scheme
M1: converts to a common denominator or decimals (3/8 and 4/8, or 0.375 and 0.5); A1: No, 3/8 < 1/2
Model answer
No. 1/2 = 4/8 and 3/8 < 4/8, so 3/8 is less than 1/2. (As decimals, 0.375 < 0.5.) A larger denominator means smaller pieces.
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