Solved Exercises on Addition of Tenths and Hundredths in Grade 4

Master addition of tenths and hundredths: rules for adding fractions with denominators 10 and 100 through these 5 detailed exercises with visual representations.

Solution: Exercises 1 to 3
1 Adding tenths with tenths
Exercise 1
Calculate: \(\frac{3}{10} + \frac{4}{10}\)
Definition:

Tenths: Fractions with denominator 10, representing one of ten equal parts of a whole

Method for adding like denominators:
  1. Verify that both fractions have the same denominator (10)
  2. Add the numerators together
  3. Keep the denominator the same
Expression
\(\frac{3}{10} + \frac{4}{10}\)
Denominator
Keep 10
Result
\(\frac{7}{10}\)
Step 1: Verify like denominators

Both fractions have denominator 10, so we can add directly

Step 2: Add the numerators

Add numerators: \(3 + 4 = 7\)

Step 3: Keep the denominator

The denominator remains 10

\(\frac{3}{10}\)
+
\(\frac{4}{10}\)
=
\(\frac{7}{10}\)
+
=
\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)
\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)
Final answer:

\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)

Applied rules:

• Addition rule: \(\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}\)

• Like denominators: When denominators are the same, add numerators directly

• Denominator preservation: The denominator remains unchanged in the result

2 Adding hundredths with hundredths
Exercise 2
Calculate: \(\frac{25}{100} + \frac{34}{100}\)
Definition:

Hundredths: Fractions with denominator 100, representing one of one hundred equal parts of a whole

Expression
\(\frac{25}{100} + \frac{34}{100}\)
Denominator
Keep 100
Result
\(\frac{59}{100}\)
Step 1: Verify like denominators

Both fractions have denominator 100, so we can add directly

Step 2: Add the numerators

Add numerators: \(25 + 34 = 59\)

Step 3: Keep the denominator

The denominator remains 100

\(\frac{25}{100}\)
+
\(\frac{34}{100}\)
=
\(\frac{59}{100}\)
+
=
Addition of Tenths and Hundredths | Solved Exercises | Mathematics Grade 4

Solved Exercises on Addition of Tenths and Hundredths in Grade 4

Master addition of tenths and hundredths: rules for adding fractions with denominators 10 and 100 through these 5 detailed exercises with visual representations.

Solution: Exercises 1 to 3
1 Adding tenths to tenths
Exercise 1
Calculate: \(\frac{3}{10} + \frac{4}{10}\)
Definition:

Tenths: Fractions with denominator 10, representing one part out of ten equal parts

Method for adding tenths:
  1. Keep the same denominator (10)
  2. Add the numerators together
  3. Write the result as a new fraction
Expression
\(\frac{3}{10} + \frac{4}{10}\)
Denominator
Keep 10
Result
\(\frac{7}{10}\)
Step 1: Verify like denominators

Both fractions have denominator 10, so we can add directly

Step 2: Add the numerators

Add numerators: \(3 + 4 = 7\)

Step 3: Keep the denominator

The denominator remains 10

\(\frac{3}{10}\)
+
\(\frac{4}{10}\)
=
\(\frac{7}{10}\)
\(\frac{3}{10} + \frac{4}{10} = \frac{3+4}{10} = \frac{7}{10}\)
\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)
Final answer:

\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)

Applied rules:

• Addition rule: \(\frac{a}{10} + \frac{b}{10} = \frac{a+b}{10}\)

• Like denominators: When denominators are the same, add numerators directly

• Denominator preservation: The denominator remains unchanged in the result

2 Adding tenths and hundredths
Exercise 2
Calculate: \(\frac{2}{10} + \frac{15}{100}\)
Definition:

Hundredths: Fractions with denominator 100, representing one part out of one hundred equal parts

Expression
\(\frac{2}{10} + \frac{15}{100}\)
Convert to 100
\(\frac{20}{100} + \frac{15}{100}\)
Result
\(\frac{35}{100}\)
Step 1: Convert tenths to hundredths

\(\frac{2}{10} = \frac{2 \times 10}{10 \times 10} = \frac{20}{100}\)

Step 2: Add the fractions

\(\frac{20}{100} + \frac{15}{100} = \frac{35}{100}\)

Step 3: Simplify if needed

\(\frac{35}{100} = \frac{7}{20}\)

\(\frac{2}{10}\)
+
\(\frac{15}{100}\)
=
\(\frac{20}{100}\)
+
\(\frac{15}{100}\)
=
\(\frac{35}{100}\)
Conversion:
\(\frac{2}{10} = \frac{20}{100}\) because 1 tenth = 10 hundredths
Addition of Tenths and Hundredths | Solved Exercises | Mathematics Grade 4

Solved Exercises on Addition of Tenths and Hundredths in Grade 4

Master addition of tenths and hundredths: rules for adding fractions with denominators 10 and 100 through these 5 detailed exercises with visual representations.

Solution: Exercises 1 to 3
1 Adding tenths with tenths
Exercise 1
Calculate: \(\frac{3}{10} + \frac{4}{10}\)
Definition:

Tenths: Fractions with denominator 10, representing one of ten equal parts of a whole

Method for adding like denominators:
  1. Verify that both fractions have the same denominator (10)
  2. Add the numerators together
  3. Keep the denominator the same
Expression
\(\frac{3}{10} + \frac{4}{10}\)
Denominator
Keep 10
Result
\(\frac{7}{10}\)
Step 1: Verify like denominators

Both fractions have denominator 10, so we can add directly

Step 2: Add the numerators

Add numerators: \(3 + 4 = 7\)

Step 3: Keep the denominator

The denominator remains 10

\(\frac{3}{10}\)
+
\(\frac{4}{10}\)
=
\(\frac{7}{10}\)
+
=
\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)
\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)
Final answer:

\(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\)

Applied rules:

• Addition rule: \(\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}\)

• Like denominators: When denominators are the same, add numerators directly

• Denominator preservation: The denominator remains unchanged in the result

2 Adding hundredths with hundredths
Exercise 2
Calculate: \(\frac{25}{100} + \frac{34}{100}\)
Definition:

Hundredths: Fractions with denominator 100, representing one of one hundred equal parts of a whole

Expression
\(\frac{25}{100} + \frac{34}{100}\)
Denominator
Keep 100
Result
\(\frac{59}{100}\)
Step 1: Verify like denominators

Both fractions have denominator 100, so we can add directly

Step 2: Add the numerators

Add numerators: \(25 + 34 = 59\)

Step 3: Keep the denominator

The denominator remains 100

\(\frac{25}{100}\)
+
\(\frac{34}{100}\)
=
\(\frac{59}{100}\)
+
=