Question
Write these numbers in order, starting with the smallest.
$$0.45\quad \quad \quad 42\%\quad \quad \quad \frac4{11}\quad \quad \quad \frac25$$
▶️Answer/Explanation
$\frac 4{11}$ $\frac 25$ $42\% 0. 45$
\( 0.45 \) is already a decimal.
\( 42\% = 0.42 \) (since percent means “out of 100”)
\( \frac{4}{11} \approx 0.3636 \) (divide 4 by 11)
\( \frac{2}{5} = 0.4 \)
$
0.3636, \quad 0.4, \quad 0.42, \quad 0.45
$
From smallest to largest
$
\frac{4}{11}, \quad \frac{2}{5}, \quad 42\%, \quad 0.45
$
Question
Write these numbers in order, starting with the smallest.
$\frac{6}{7}$ $8.6\times 10^{-1}$ $\frac{11}{13}$ $86.5\%$
▶️Answer/Explanation
$\frac {11}{13}$ $\frac{6}{7}$ $8. 6\times 10^{- 1}$ $86. 5\%$
1. \( \frac{6}{7} \approx 0.857 \)
2. \( 8.6 \times 10^{-1} = 0.86 \)
3. \( \frac{11}{13} \approx 0.846 \)
4. \( 86.5\% = 0.865 \)
order them from smallest to largest
$
\frac{11}{13} \approx 0.846, \quad \frac{6}{7} \approx 0.857, \quad 8.6 \times 10^{-1} = 0.86, \quad 86.5\% = 0.865
$
Finally:
$
\frac{11}{13}, \quad \frac{6}{7}, \quad 8.6 \times 10^{-1}, \quad 86.5\%
$
Question
Write \($0.70\) as a fraction of \($5.60\), giving your answer in its lowest terms.
▶️Answer/Explanation
To write \($0.70\) as a fraction of \($5.60\),we divide\( $0.70 \)by \($5.60 ,\)
\(\frac{$0.70}{$5.60}=\frac{70}{560}=\frac{1}{8}\)
Question
(a) Work out \(\frac{5}{12}\) of 168.
▶️Answer/Explanation
To work out \(\frac{5}{12}\) of 168, we can multiply 168 by\(\frac{5}{12}\),which gives:
\(\frac{5}{12}\times 168=\frac{5\times 168}{12}=70\)
Therefore, \(\frac{5}{12}\) of 168 is 70.
(b) Write \(\frac{3}{8}\) as a decimal.
▶️Answer/Explanation
To convert \(\frac{3}{8}\) to a decimal, we need to perform the division 3 divided by 8.
So \(\frac{3}{8}\) as a decimal is 0.375.
Question
Without using a calculator, work out \(\frac{6}{7} \div 1 \frac{2}{3}\)
Show all your working and give your answer as a fraction in its lowest terms.
▶️Answer/Explanation
To divide \(\frac{6}{7}\) by\(1\frac{2}{3}\),we first need to convert the mixed number to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator.
\(1\frac{2}{3}=\frac{1\times 3+2}{3}\)
\(=\frac{5}{3}\)
So we need to divide\( \frac{6}{7}\) by\( \frac{5}{3}.\)
When dividing fractions, we can use the rule,
\(\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}.\)
\(\therefore \frac{6}{7}\div \frac{5}{3}=\frac{6}{7}\times \frac{3}{5}\)
\(\Rightarrow\)
\(\frac{6}{7} \times \frac{3}{5} = \frac{2\times 3}{7} \times \frac{3}{5}\)
\(= \frac{2\times 3\times 3}{7\times 5}\)
\(= \frac{18}{35}\)
So,\(\frac{6}{7}\div 1\frac{2}{3}=\frac{18}{35}.\)
Question
Write down the difference in temperature between -4 °C and -9 °C.
………………………………………. °C
▶️Answer/Explanation
To find the difference in temperature between -4°C and -9°C, we need to subtract the smaller temperature from the larger temperature.Hence, -9°C is the smaller temperature and -4°C is the larger temperature.
So the difference in temperature is,
-4°C – (-9°C) &= -4°C + 9°C
= 5°C
Therefore, the difference in temperature between -4°C and -9°C is 5°C.