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2 (a) Work out - OCR - GCSE Maths - Question 2 - 2017 - Paper 1

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2 (a) Work out. (i) 6 \frac{1}{2} + \frac{3}{4} (ii) \frac{4}{7} of 63 (b) Show that \frac{4}{5} is bigger than \frac{7}{9}.

Worked Solution & Example Answer:2 (a) Work out - OCR - GCSE Maths - Question 2 - 2017 - Paper 1

Step 1

(i) 6 \frac{1}{2} + \frac{3}{4}

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Answer

To solve this, we first convert the mixed number into an improper fraction:

612=12+12=1326 \frac{1}{2} = \frac{12 + 1}{2} = \frac{13}{2}

Next, we find a common denominator for \frac{13}{2} and \frac{3}{4} which is 4:

  • Convert \frac{13}{2} to have a denominator of 4:
132=13×22×2=264\frac{13}{2} = \frac{13 \times 2}{2 \times 2} = \frac{26}{4}

Now we can add:

264+34=294\frac{26}{4} + \frac{3}{4} = \frac{29}{4}

The result is \frac{29}{4} or 7 \frac{1}{4}.

Step 2

(ii) \frac{4}{7} of 63

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Answer

To calculate \frac{4}{7} of 63, we multiply 63 by \frac{4}{7}:

47⋅63=4⋅637=2527=36\frac{4}{7} \cdot 63 = \frac{4 \cdot 63}{7} = \frac{252}{7} = 36

So \frac{4}{7} of 63 is 36.

Step 3

(b) Show that \frac{4}{5} is bigger than \frac{7}{9}.

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Answer

To compare \frac{4}{5} and \frac{7}{9}, we find a common denominator. The least common multiple of 5 and 9 is 45.

Now we convert both fractions:

45=4×95×9=3645\frac{4}{5} = \frac{4 \times 9}{5 \times 9} = \frac{36}{45} 79=7×59×5=3545\frac{7}{9} = \frac{7 \times 5}{9 \times 5} = \frac{35}{45}

Now we can compare:

3645>3545\frac{36}{45} > \frac{35}{45}

Thus, \frac{4}{5} is indeed bigger than \frac{7}{9}.

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