Find the sums and differences: (a) (b) (c) (d) (e) (f)

We will convert all numbers to decimal form. This makes adding and subtracting very easy. Step 1 — Calculate (a) We need to find the sum of and . First, we convert to a decimal. Next, we convert to a decimal. Now, we add these two decimal numbers. > Step 2 — Calculate (b) We need to find the sum of and . First, we convert to a decimal. This means 9 whole units, 5 tenths, and 7 hundredths. Next, we convert to a decimal. This means 2 whole units, 1 tenth, and 3 hundredths. Now, we add these two decimal numbers. > Step 3 — Calculate (c) We need to find the sum of and . First, we convert to a decimal. This means 15 whole units, 6 tenths, and 4 hundredths. Next, we convert to a decimal. This means 14 whole units, 3 tenths, and 6 hundredths. Now, we add these two decimal numbers. > Step 4 — Calculate (d) We need to find the difference between and . First, we convert to a decimal. Next, we convert to a decimal. Now, we subtract the second decimal from the first. > Step 5 — Calculate (e) We need to find the difference between and . First, we convert to a decimal. Next, we convert to a decimal. Now, we subtract the second decimal from the first. > Step 6 — Calculate (f) We need to find the difference between and . First, we convert to a decimal. This means 12 whole units, 6 hundredths, and 2 hundredths. Next, we convert to a decimal. This means 9 tenths and 9 hundredths. Now, we subtract the second decimal from the first. > Answer > (a) > (b) > (c) > (d) > (e) > (f)

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Question 1

Find the sums and differences:

(a) $\frac{3}{10} + 3 \frac{4}{100}$

(b) $9 \frac{5}{10} \frac{7}{100} + 2 \frac{1}{10} \frac{3}{100}$

(d) $7 \frac{7}{100} - 4 \frac{4}{100}$

(e) $8 \frac{6}{100} - 5 \frac{3}{100}$

(f) $12 \frac{6}{100} \frac{2}{100} - \frac{9}{10} \frac{9}{100}$

Solution

We will convert all numbers to decimal form. This makes adding and subtracting very easy.

Step 1 — Calculate (a) We need to find the sum of $\frac{3}{10}$ and $3 \frac{4}{100}$ . First, we convert $\frac{3}{10}$ to a decimal. $\frac{3}{10} = 0.3$ Next, we convert $3 \frac{4}{100}$ to a decimal. $3 \frac{4}{100} = 3 + \frac{4}{100} = 3.04$ Now, we add these two decimal numbers. $0.3 + 3.04$ $= 0.30 + 3.04$

$\boxed{\mathbf{3.34}}$

Step 2 — Calculate (b) We need to find the sum of $9 \frac{5}{10} \frac{7}{100}$ and $2 \frac{1}{10} \frac{3}{100}$ . First, we convert $9 \frac{5}{10} \frac{7}{100}$ to a decimal. This means 9 whole units, 5 tenths, and 7 hundredths. $9 \frac{5}{10} \frac{7}{100} = 9 + 0.5 + 0.07 = 9.57$ Next, we convert $2 \frac{1}{10} \frac{3}{100}$ to a decimal. This means 2 whole units, 1 tenth, and 3 hundredths. $2 \frac{1}{10} \frac{3}{100} = 2 + 0.1 + 0.03 = 2.13$ Now, we add these two decimal numbers. $9.57 + 2.13$ $= \mathbf{11.70}$

$\boxed{\mathbf{11.70}}$

Step 3 — Calculate (c) We need to find the sum of $15 \frac{6}{10} \frac{4}{100}$ and $14 \frac{3}{10} \frac{6}{100}$ . First, we convert $15 \frac{6}{10} \frac{4}{100}$ to a decimal. This means 15 whole units, 6 tenths, and 4 hundredths. $15 \frac{6}{10} \frac{4}{100} = 15 + 0.6 + 0.04 = 15.64$ Next, we convert $14 \frac{3}{10} \frac{6}{100}$ to a decimal. This means 14 whole units, 3 tenths, and 6 hundredths. $14 \frac{3}{10} \frac{6}{100} = 14 + 0.3 + 0.06 = 14.36$ Now, we add these two decimal numbers. $15.64 + 14.36$ $= \mathbf{30.00}$

$\boxed{\mathbf{30.00}}$

Step 4 — Calculate (d) We need to find the difference between $7 \frac{7}{100}$ and $4 \frac{4}{100}$ . First, we convert $7 \frac{7}{100}$ to a decimal. $7 \frac{7}{100} = 7 + \frac{7}{100} = 7.07$ Next, we convert $4 \frac{4}{100}$ to a decimal. $4 \frac{4}{100} = 4 + \frac{4}{100} = 4.04$ Now, we subtract the second decimal from the first. $7.07 - 4.04$ $= \mathbf{3.03}$

$\boxed{\mathbf{3.03}}$

Step 5 — Calculate (e) We need to find the difference between $8 \frac{6}{100}$ and $5 \frac{3}{100}$ . First, we convert $8 \frac{6}{100}$ to a decimal. $8 \frac{6}{100} = 8 + \frac{6}{100} = 8.06$ Next, we convert $5 \frac{3}{100}$ to a decimal. $5 \frac{3}{100} = 5 + \frac{3}{100} = 5.03$ Now, we subtract the second decimal from the first. $8.06 - 5.03$ $= \mathbf{3.03}$

$\boxed{\mathbf{3.03}}$

Step 6 — Calculate (f) We need to find the difference between $12 \frac{6}{100} \frac{2}{100}$ and $\frac{9}{10} \frac{9}{100}$ . First, we convert $12 \frac{6}{100} \frac{2}{100}$ to a decimal. This means 12 whole units, 6 hundredths, and 2 hundredths. $12 \frac{6}{100} \frac{2}{100} = 12 + 0.06 + 0.02 = 12.08$ Next, we convert $\frac{9}{10} \frac{9}{100}$ to a decimal. This means 9 tenths and 9 hundredths. $\frac{9}{10} \frac{9}{100} = 0.9 + 0.09 = 0.99$ Now, we subtract the second decimal from the first. $12.08 - 0.99$ $= \mathbf{11.09}$

$\boxed{\mathbf{11.09}}$

Answer

(a) $\mathbf{3.34}$ (b) $\mathbf{11.70}$ (c) $\mathbf{30.00}$ (d) $\mathbf{3.03}$ (e) $\mathbf{3.03}$ (f) $\mathbf{11.09}$