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13 (a) Calculate - OCR - GCSE Maths - Question 13 - 2018 - Paper 1
Question 13
13 (a) Calculate. \( \frac{3}{5} + \frac{5}{8} \) Give your answer as a mixed number in its simplest form. (b) Work out. \( 5 \times 10^4 - 1.6 \times 10^3 \) G... show full transcript
Worked Solution & Example Answer:13 (a) Calculate - OCR - GCSE Maths - Question 13 - 2018 - Paper 1
Step 1
Calculate. \( \frac{3}{5} + \frac{5}{8} \)
Answer
To add the fractions ( \frac{3}{5} ) and ( \frac{5}{8} ), we first need a common denominator.
The least common denominator (LCD) of 5 and 8 is 40. We convert each fraction:
[ \frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40} ]
[ \frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40} ]
Now we can add the fractions:
[ \frac{24}{40} + \frac{25}{40} = \frac{49}{40} ]
To express ( \frac{49}{40} ) as a mixed number:
[ \frac{49}{40} = 1 \frac{9}{40} ]
Thus, the answer is ( 1 \frac{9}{40} ).
Step 2
Work out. \( 5 \times 10^4 - 1.6 \times 10^3 \)
Answer
To perform the subtraction, we convert the terms into standard form with the same exponent:
( 5 \times 10^4 ) is already in standard form.
For ( 1.6 \times 10^3 ), we can convert it to have the same exponent:
[ 1.6 \times 10^3 = 0.16 \times 10^4 ]
Now our expression is:
[ 5 \times 10^4 - 0.16 \times 10^4 = (5 - 0.16) \times 10^4 = 4.84 \times 10^4 ]
Thus, the final answer in standard form is ( 4.84 \times 10^4 ).