Question

adding and subtracting fractions with different denominators

1. raul walked $12\frac{6}{7}$ km on monday. he walked $8\frac{2}{3}$ more on friday. how many more km did he walk on monday than on friday?

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1. emily measured her mum and dad. her mum was $1\frac{2}{3}$ metres tall and her dad was $1\frac{6}{8}$ metres tall. how much taller is her dad than her mum?

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1. juno bought two books. the first book weighed $1\frac{2}{5}$ kg. the second book weighed $1\frac{5}{6}$ kg. how much do the books weigh in total?

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Explanation:

Problem 6

Step1: Identify the distances

Monday: $12\frac{6}{7}$ km, Friday: $8\frac{2}{3}$ km.

Step2: Subtract Friday's distance from Monday's

First, convert mixed numbers to improper fractions:
$12\frac{6}{7} = \frac{12\times7 + 6}{7} = \frac{90}{7}$
$8\frac{2}{3} = \frac{8\times3 + 2}{3} = \frac{26}{3}$

Step3: Find a common denominator (21)

$\frac{90}{7} = \frac{90\times3}{7\times3} = \frac{270}{21}$
$\frac{26}{3} = \frac{26\times7}{3\times7} = \frac{182}{21}$

Step4: Subtract the fractions

$\frac{270}{21} - \frac{182}{21} = \frac{270 - 182}{21} = \frac{88}{21}$

Step5: Convert back to mixed number

$\frac{88}{21} = 4\frac{4}{21}$

Step1: Identify the heights

Mum: $1\frac{2}{3}$ m, Dad: $1\frac{6}{8}$ m (simplify $\frac{6}{8}$ to $\frac{3}{4}$: $1\frac{3}{4}$ m)

Step2: Subtract mum's height from dad's

Convert to improper fractions:
$1\frac{2}{3} = \frac{5}{3}$, $1\frac{3}{4} = \frac{7}{4}$

Step3: Find common denominator (12)

$\frac{5}{3} = \frac{20}{12}$, $\frac{7}{4} = \frac{21}{12}$

Step4: Subtract

$\frac{21}{12} - \frac{20}{12} = \frac{1}{12}$

Step1: Identify the weights

First book: $1\frac{2}{5}$ kg, Second book: $1\frac{5}{6}$ kg.

Step2: Add the weights

Convert to improper fractions:
$1\frac{2}{5} = \frac{7}{5}$, $1\frac{5}{6} = \frac{11}{6}$

Step3: Find common denominator (30)

$\frac{7}{5} = \frac{42}{30}$, $\frac{11}{6} = \frac{55}{30}$

Step4: Add the fractions

$\frac{42}{30} + \frac{55}{30} = \frac{97}{30}$

Step5: Convert back to mixed number

$\frac{97}{30} = 3\frac{7}{30}$

Answer:

$4\frac{4}{21}$ km

Problem 7