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

Understand the Question Fractions with denominators and represent decimal place values: (tenths place) (hundredths place) Mixed place-value notations represent the sum of their whole number and fractional parts, e.g., . Converting each expression to its standard decimal form allows us to add or subtract directly by aligning the decimal points. Part (a) Step 1 · Convert to Decimals and Add Convert each term to decimal form: Add the decimal values: Answer > (a) Part (b) Step 1 · Convert to Decimals and Add Convert each term to decimal form: Add the decimal values: Answer > (b) Part (c) Step 1 · Convert to Decimals and Add Convert each term to decimal form: Add the decimal values: Answer > (c) Part (d) Step 1 · Convert to Decimals and Subtract Convert each term to decimal form: Subtract the decimal values: Answer > (d) Part (e) Step 1 · Convert to Decimals and Subtract Convert each term to decimal form: Subtract the decimal values: Answer > (e) Part (f) Step 1 · Convert to Decimals and Subtract Convert each term to decimal form: Subtract the decimal values: Answer > (f) Common Mistakes Place Value Misplacement: Writing as instead of . Remember that the hundredths place is the second digit after the decimal point. Misaligned Decimal Addition: Writing by failing to pad to before adding.

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Question 1

Find the sums and differences:

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

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

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

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

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

Solution

Understand the Question

Fractions with denominators $10$ $10$ and $100$ $100$ represent decimal place values:
- $\dfrac{1}{10} = 0.1$ (tenths place)
- $\dfrac{1}{100} = 0.01$ (hundredths place)
Mixed place-value notations represent the sum of their whole number and fractional parts, e.g., $9\dfrac{5}{10}\dfrac{7}{100} = 9 + 0.5 + 0.07 = 9.57$ .
Converting each expression to its standard decimal form allows us to add or subtract directly by aligning the decimal points.

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

Step 1 · Convert to Decimals and Add

Convert each term to decimal form: $\dfrac{3}{10} = 0.3$ $3 \dfrac{4}{100} = 3 + \dfrac{4}{100} = 3.04$

Add the decimal values:

\begin{aligned} 0.3 + 3.04 &= 0.30 + 3.04 \\[0.6em] &= 3.34 \end{aligned}

Answer

(a) $3.34$

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

Step 1 · Convert to Decimals and Add

Convert each term to decimal form: $9 \dfrac{5}{10} \dfrac{7}{100} = 9 + 0.5 + 0.07 = 9.57$ $2 \dfrac{1}{10} \dfrac{3}{100} = 2 + 0.1 + 0.03 = 2.13$

Add the decimal values: $9.57 + 2.13 = 11.70$

Answer

(b) $11.70$

(c) $15 \dfrac{6}{10} \dfrac{4}{100} + 14 \dfrac{3}{10} \dfrac{6}{100}$

Step 1 · Convert to Decimals and Add

Convert each term to decimal form: $15 \dfrac{6}{10} \dfrac{4}{100} = 15 + 0.6 + 0.04 = 15.64$ $14 \dfrac{3}{10} \dfrac{6}{100} = 14 + 0.3 + 0.06 = 14.36$

Add the decimal values: $15.64 + 14.36 = 30.00$

Answer

(c) $30.00$

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

Step 1 · Convert to Decimals and Subtract

Convert each term to decimal form: $7 \dfrac{7}{100} = 7 + \dfrac{7}{100} = 7.07$ $4 \dfrac{4}{100} = 4 + \dfrac{4}{100} = 4.04$

Subtract the decimal values: $7.07 - 4.04 = 3.03$

Answer

(d) $3.03$

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

Step 1 · Convert to Decimals and Subtract

Convert each term to decimal form: $8 \dfrac{6}{100} = 8 + \dfrac{6}{100} = 8.06$ $5 \dfrac{3}{100} = 5 + \dfrac{3}{100} = 5.03$

Subtract the decimal values: $8.06 - 5.03 = 3.03$

Answer

(e) $3.03$

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

Step 1 · Convert to Decimals and Subtract

Convert each term to decimal form: $12 \dfrac{6}{100} \dfrac{2}{100} = 12 + 0.06 + 0.02 = 12.08$ $\dfrac{9}{10} \dfrac{9}{100} = 0.9 + 0.09 = 0.99$

Subtract the decimal values: $12.08 - 0.99 = 11.09$

Answer

(f) $11.09$

Common Mistakes

Place Value Misplacement: Writing $\dfrac{4}{100}$ as $0.4$ instead of $0.04$ . Remember that the hundredths place is the second digit after the decimal point.
Misaligned Decimal Addition: Writing $0.3 + 3.04 = 3.07$ by failing to pad $0.3$ to $0.30$ before adding.