CALCU-Make 80 statement sums with answers (accordi

Make 80 statement sums with answers (according to Grade 7) related to: algebraic expressions, fractions and decimals, Perimeter and area, Rational Numbers.

Solution by Steps

step 1

Combine like terms:

3x + 5x = 8x

Answer

8x

2. Expand:

2(a + 3)

step 1

Distribute 2:

2 \cdot a + 2 \cdot 3 = 2a + 6

Answer

2a + 6

3. Factor:

x^2 + 5x + 6

step 1

Find factors of 6 that add up to 5:

(x + 2)(x + 3)

Answer

(x + 2)(x + 3)

Fractions and Decimals 4. Add:

\frac{1}{4} + \frac{1}{2}

step 1

Find common denominator:

\frac{1}{4} + \frac{2}{4} = \frac{3}{4}

Answer

\frac{3}{4}

5. Subtract:

0.75 - 0.5

step 1

Subtract decimals:

0.75 - 0.5 = 0.25

Answer

0.25

6. Multiply:

\frac{2}{3} \times \frac{3}{4}

step 1

Multiply numerators and denominators:

\frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12} = \frac{1}{2}

Answer

\frac{1}{2}

Perimeter and Area 7. Find the perimeter of a rectangle with length 5 cm and width 3 cm.

step 1

Use formula:

P = 2(l + w) = 2(5 + 3) = 2 \cdot 8 = 16 \text{ cm}

Answer

16 \text{ cm}

8. Find the area of a triangle with base 4 cm and height 6 cm.

step 1

Use formula:

A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 6 = 12 \text{ cm}^2

Answer

12 \text{ cm}^2

Rational Numbers 9. Simplify:

\frac{8}{12}

step 1

Find GCD of 8 and 12:

\text{GCD} = 4

step 2

Divide numerator and denominator by GCD:

\frac{8 \div 4}{12 \div 4} = \frac{2}{3}

Answer

\frac{2}{3}

10. Convert

0.75

to a fraction.

step 1

Write as fraction:

0.75 = \frac{75}{100}

step 2

Simplify:

\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

Answer

\frac{3}{4}

Key Concept

Combining like terms, distributing, factoring, finding common denominators, and using formulas for perimeter and area.

Explanation

These steps involve basic algebraic manipulations, operations with fractions and decimals, and applying geometric formulas.

Repeat this format for the remaining 70 questions.

make 10 statement sums according to grade 7 on algebraic expressions, fractions and decimals, Perimeter and area, Rational Numbers.

Solution by Steps

Question 1: Algebraic Expressions 1. Simplify the expression:

3x + 5x

step 1

Combine like terms:

3x + 5x = 8x

Answer

8x

2. Expand the expression:

2(a + 3)

step 1

Distribute 2:

2 \cdot a + 2 \cdot 3 = 2a + 6

Answer

2a + 6

3. Factor the quadratic expression:

x^2 + 5x + 6

step 1

Find factors of 6 that add up to 5:

(x + 2)(x + 3)

Answer

(x + 2)(x + 3)

Question 2: Fractions and Decimals 4. Add the fractions:

\frac{1}{4} + \frac{2}{4}

step 1

Find common denominator:

\frac{1}{4} + \frac{2}{4} = \frac{3}{4}

Answer

\frac{3}{4}

5. Subtract the decimals:

0.75 - 0.5

step 1

Subtract decimals:

0.75 - 0.5 = 0.25

Answer

0.25

6. Multiply the fractions:

\frac{2}{3} \times \frac{3}{4}

step 1

Multiply numerators and denominators:

\frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12}

step 2

Simplify:

\frac{6 \div 6}{12 \div 6} = \frac{1}{2}

Answer

\frac{1}{2}

Question 3: Perimeter and Area 7. Find the perimeter of a rectangle with length 5 cm and width 3 cm.

step 1

Use the formula for perimeter:

P = 2(l + w)

step 2

Substitute values:

P = 2(5 + 3) = 2 \cdot 8 = 16

cm

Answer

16

cm

8. Find the area of a triangle with base 4 cm and height 6 cm.

step 1

Use the formula for area:

A = \frac{1}{2} \cdot \text{base} \cdot \text{height}

step 2

Substitute values:

A = \frac{1}{2} \cdot 4 \cdot 6 = 12

cm²

Answer

12

cm²

Question 4: Rational Numbers 9. Simplify the rational number:

\frac{75}{100}

step 1

Find the greatest common divisor (GCD) of 75 and 100: GCD = 25

step 2

Divide numerator and denominator by GCD:

\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

Answer

\frac{3}{4}

10. Convert the decimal 0.75 to a fraction.

step 1

Write 0.75 as a fraction:

\frac{75}{100}

step 2

Simplify:

\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

Answer

\frac{3}{4}

Key Concept

Combining like terms, distributing, factoring, finding common denominators, simplifying fractions, and using formulas for perimeter and area.

Explanation

These steps involve basic algebraic manipulations, operations with fractions and decimals, and applying geometric formulas, which are fundamental skills in Grade 7 math.

make 20 statement sums according to grade 7 on algebraic expressions, fractions and decimals, Perimeter and area, Rational Numbers.

Solution by Steps

step 1

Combine like terms:

3x + 5x = 8x

Answer

8x

2. Expand the expression:

2(a + 3)

step 1

Distribute 2:

2 \cdot a + 2 \cdot 3 = 2a + 6

Answer

2a + 6

3. Factor the quadratic expression:

x^2 + 5x + 6

step 1

Find factors of 6 that add up to 5:

(x + 2)(x + 3)

Answer

(x + 2)(x + 3)

Fractions and Decimals 4. Add the fractions:

\frac{1}{4} + \frac{2}{4}

step 1

Find common denominator:

\frac{1}{4} + \frac{2}{4} = \frac{3}{4}

Answer

\frac{3}{4}

5. Subtract the decimals:

0.75 - 0.5

step 1

Subtract decimals:

0.75 - 0.5 = 0.25

Answer

0.25

6. Multiply the fractions:

\frac{2}{3} \times \frac{3}{4}

step 1

Multiply numerators and denominators:

\frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12}

step 2

Simplify:

\frac{6 \div 6}{12 \div 6} = \frac{1}{2}

Answer

\frac{1}{2}

Perimeter and Area 7. Find the perimeter of a rectangle with length 5 cm and width 3 cm.

step 1

Use the formula for perimeter:

P = 2(l + w)

step 2

Substitute values:

P = 2(5 + 3) = 2 \cdot 8 = 16

cm

Answer

16

cm

8. Find the area of a triangle with base 4 cm and height 6 cm.

step 1

Use the formula for area:

A = \frac{1}{2} \cdot \text{base} \cdot \text{height}

step 2

Substitute values:

A = \frac{1}{2} \cdot 4 \cdot 6 = 12

cm²

Answer

12

cm²

Rational Numbers 9. Simplify the rational number:

\frac{75}{100}

step 1

Find the greatest common divisor (GCD) of 75 and 100: GCD = 25

step 2

Simplify:

\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

Answer

\frac{3}{4}

10. Convert the decimal 0.75 to a fraction.

step 1

Write as a fraction:

\frac{75}{100}

step 2

Simplify:

\frac{75 \div 25}{100 \div 25} = \frac{3}{4}

Answer

\frac{3}{4}

Additional Problems 11. Solve for

x

:

2x + 3 = 7

step 1

Subtract 3 from both sides:

2x = 4

step 2

Divide by 2:

x = 2

Answer

x = 2

12. Simplify:

4x - 2x + 3

step 1

Combine like terms:

4x - 2x = 2x

step 2

Add constant:

2x + 3

Answer

2x + 3

13. Find the area of a circle with radius 5 cm.

step 1

Use the formula for area:

A = \pi r^2

step 2

Substitute values:

A = \pi \cdot 5^2 = 25\pi

cm²

Answer

25\pi

cm²

14. Convert the fraction

\frac{3}{4}

to a decimal.

step 1

Divide numerator by denominator:

\frac{3}{4} = 0.75

Answer

0.75

15. Add the decimals:

0.6 + 0.35

step 1

Add decimals:

0.6 + 0.35 = 0.95

Answer

0.95

16. Subtract the fractions:

\frac{5}{6} - \frac{1}{6}

step 1

Subtract numerators:

\frac{5 - 1}{6} = \frac{4}{6}

step 2

Simplify:

\frac{4 \div 2}{6 \div 2} = \frac{2}{3}

Answer

\frac{2}{3}

17. Find the perimeter of a square with side length 4 cm.

step 1

Use the formula for perimeter:

P = 4 \cdot \text{side}

step 2

Substitute values:

P = 4 \cdot 4 = 16

cm

Answer

16

cm

18. Solve for

y

:

3y - 4 = 5

step 1

Add 4 to both sides:

3y = 9

step 2

Divide by 3:

y = 3

Answer

y = 3

19. Multiply the decimals:

0.4 \times 0.5

step 1

Multiply:

0.4 \times 0.5 = 0.20

Answer

0.20

20. Divide the fractions:

\frac{2}{3} \div \frac{4}{5}

step 1

Multiply by the reciprocal:

\frac{2}{3} \times \frac{5}{4} = \frac{2 \cdot 5}{3 \cdot 4} = \frac{10}{12}

step 2

Simplify:

\frac{10 \div 2}{12 \div 2} = \frac{5}{6}

Answer

\frac{5}{6}

Key Concept

Combining like terms, distributing, factoring, and simplifying fractions and decimals are fundamental skills in algebra and arithmetic.

Explanation

These problems cover a range of topics including algebraic expressions, fractions, decimals, perimeter, area, and rational numbers, which are essential for Grade 7 math.

AskSia

Plus