Units and Fractions

Conversions and Units

Converting and Calculating Units of Length

Converting and Calculating Units of Mass

Calculating Money

Converting Time and Calculating Time

Fractions

Introduction to Fractions

Equivalent Fractions

Comparing Fractions

Adding and Subtracting Fractions

Multiplying Fractions

Dividing Fractions

Calculating Fractions and Decimals

Ratios, Percentages, Proportions

Fractions and Ratios

Fractions and Percentages

Percentage Calculation

Interest and Interest Rate Calculation

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Directly Proportional and Inversely Proportional

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Calculating Fractions and Decimals

Units and Fractions Calculating Fractions and Decimals

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(0:01) Recap of Commutative and Associative Laws:The commutative law lets you rearrange terms, while the associative law allows grouping them.
(0:16) Commutative and Associative Laws For Fractions and Decimals: Group similar terms (e.g., decimals together, fractions together) to simplify calculations faster.
(2:07) Distributive Law with Decimals and Fractions: Factor out common terms using the distributive law to simplify multi-step calculations.

📂 Revision Cards

Showing the commutative law (a + b = b + a), associative law (a + (b + c) = (a + b) + c), and distributive law (a × (b + c) = ab + ac) — 1) Properties of Arithmetic (Formulas)

Example of the commutative and associative laws in addition with decimals and fractions, showing rearrangement and grouping of numbers. — 2) Commutative and Associative Law in Addition

Commutative and associative laws in multiplication shown with a worked example involving fractions, decimals, and whole numbers. — 3) Commutative and Associative Law in Multiplication

Distributive law example using 6 × (2.3 ? 5/6), showing step-by-step calculation with decimals and fractions, ending with 8.8. — 4) Distributive Law with Decimals and Fractions

Explanation of distributive law applied to fractions and decimals, showing step-by-step simplification example. — 5) Distributive Law with More Terms

🍪 Quiz Time - Practice Now!

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Calculating Fractions and Decimals

1 / 6

Q:Simplify: $0.5 + \frac{2}{5} + 0.4 + \frac{1}{5}$.

1.5

1.4

2

1

Feedback: Not quite! First, add the decimals: $0.5 + 0.4 = 0.9$. Then, add the fractions: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5} = 0.6$. Finally, $0.9 + 0.6 = 1.5$.

Feedback: Well done! First, add the decimals: $0.5 + 0.4 = 0.9$. Then, add the fractions: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5} = 0.6$. Finally, $0.9 + 0.6 = 1.5$.

2 / 6

Q:Simplify: $\frac{4}{7} + 1.2 + \frac{3}{7} + 0.3$.

1.8

2.2

2

2.1

Feedback: Not quite! First, add the fractions: $\frac{4}{7} + \frac{3}{7} = 1$. Then, add the decimals: $1.2 + 0.3 = 1.5$. Finally, $1 + 1.5 = 2$.

Feedback: Well done! First, add the fractions: $\frac{4}{7} + \frac{3}{7} = 1$. Then, add the decimals: $1.2 + 0.3 = 1.5$. Finally, $1 + 1.5 = 2$.

3 / 6

Q:Simplify: $2.3 + \frac{5}{6} - \frac{1}{3}$.

2.8

3

3.3

2.7

Feedback: Not quite! First, simplify the fractions: $\frac{5}{6} - \frac{1}{3} = \frac{5-2}{6} = \frac{1}{2} = 0.5$. Then add: $2.3 + 0.5 = 2.8$.

Feedback: Well done! First, simplify the fractions: $\frac{5}{6} - \frac{1}{3} = \frac{5-2}{6} = \frac{1}{2} = 0.5$. Then add: $2.3 + 0.5 = 2.8$.

4 / 6

Q:Simplify: $2.4 - 1.1 + \frac{5}{8} - \frac{1}{8}$.

1.8

1.7

1.5

2

Feedback: Not quite! First, subtract the fractions: $\frac{5}{8} - \frac{1}{8} = \frac{4}{8} = 0.5$. Then, calculate the decimals: $2.4 - 1.1 = 1.3$. Finally, $1.3 + 0.5 = 1.8$.

Feedback: Well done! First, subtract the fractions: $\frac{5}{8} - \frac{1}{8} = \frac{4}{8} = 0.5$. Then, calculate the decimals: $2.4 - 1.1 = 1.3$. Finally, $1.3 + 0.5 = 1.8$.

5 / 6

Q:Simplify: $6 \times (\frac{5}{6} - 0.2)$

3.2

2.8

3.6

3.8

Feedback: Not quite! Using the distributive law: $6 \times \frac{5}{6} = 5$, and $6 \times 0.2 = 1.2$. Then subtract: $5 - 1.2 = 3.8$.

Feedback: Well done! Using the distributive law: $6 \times \frac{5}{6} = 5$, and $6 \times 0.2 = 1.2$. Then subtract: $5 - 1.2 = 3.8$.

6 / 6

Q:Simplify: $\frac{5}{6} \times 3.6 - \frac{5}{6} \times 1.8 + \frac{5}{6} \times 0.2$.

$\frac{5}{2}$

$\frac{3}{2}$

$\frac{5}{3}$

$\frac{5}{6}$

Feedback: Not quite! Factor out $\frac{5}{6}$: $\frac{5}{6} \times (3.6 - 1.8 + 0.2). Combine the terms in the brackets: $3.6 - 1.8 + 0.2 = 2$. Finally, $\frac{5}{6} \times 2 = \frac{5}{3}$.

Feedback: Well done! Factor out $\frac{5}{6}$: $\frac{5}{6} \times (3.6 - 1.8 + 0.2). Combine the terms in the brackets: $3.6 - 1.8 + 0.2 = 2$. Finally, $\frac{5}{6} \times 2 = \frac{5}{3}$.

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