Calculate and simplify if necessary. Example: 1/2 + 1/3 = 5/6. Where does the 6 come from?

Question

ScanSolve AI Tutor · Accepted Answer

Here are the calculations for each problem: a) Step 1: Find a common denominator for 1/4 and 1/2. The least common multiple of 4 and 2 is 4. Step 2: Convert 1/2 to an equivalent fraction with a denominator of 4. 1/2 = (1 × 2)/(2 × 2) = 2/4 Step 3: Add the fractions. 1/4 + 2/4 = (1+2)/(4) = 3/4 The fraction is already in its simplest form. 3/4 b) Step 1: Find a common denominator for 1/5 and 1/10. The least common multiple of 5 and 10 is 10. Step 2: Convert 1/5 to an equivalent fraction with a denominator of 10. 1/5 = (1 × 2)/(5 × 2) = 2/10 Step 3: Add the fractions. 2/10 + 1/10 = (2+1)/(10) = 3/10 The fraction is already in its simplest form. 3/10 c) Step 1: Find a common denominator for 1/3 and 1/6. The least common multiple of 3 and 6 is 6. Step 2: Convert 1/3 to an equivalent fraction with a denominator of 6. 1/3 = (1 × 2)/(3 × 2) = 2/6 Step 3: Add the fractions. 2/6 + 1/6 = (2+1)/(6) = 3/6 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3. 3/6 = (3 ÷ 3)/(6 ÷ 3) = 1/2 1/2 d) Step 1: Find a common denominator for 1/8 and 1/4. The least common multiple of 8 and 4 is 8. Step 2: Convert 1/4 to an equivalent fraction with a denominator of 8. 1/4 = (1 × 2)/(4 × 2) = 2/8 Step 3: Add the fractions. 1/8 + 2/8 = (1+2)/(8) = 3/8 The fraction is already in its simplest form. 3/8 e) Step 1: Find a common denominator for 1/5 and 1/4. The least common multiple of 5 and 4 is 20. Step 2: Convert both fractions to equivalent fractions with a denominator of 20. 1/5 = (1 × 4)/(5 × 4) = 4/20; 1/4 = (1 × 5)/(4 × 5) = 5/20 Step 3: Add the fractions. 4/20 + 5/20 = (4+5)/(20) = 9/20 The fraction is already in its simplest form. 9/20 f) Step 1: Find a common denominator for 1/2 and 1/3. The least common multiple of 2 and 3 is 6. Step 2: Convert both fractions to equivalent fractions with a denominator of 6. 1/2 = (1 × 3)/(2 × 3) = 3/6; 1/3 = (1 × 2)/(3 × 2) = 2/6 Step 3: Add the fractions. 3/6 + 2/6 = (3+2)/(6) = 5/6 The fraction is already in its simplest form. 5/6

Calculate and simplify if necessary. Example: 1/2 + 1/3 = 5/6. Where does the 6 come from?

Answers

Step-by-step solution

Part a· 3 steps

Find a common denominator for $\frac{1}{4}$ and $\frac{1}{2}$ .

Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 4.

Add the fractions.

Part b· 3 steps
$\frac{3}{10}$

Find a common denominator for $\frac{1}{5}$ and $\frac{1}{10}$ .

Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 10.

Add the fractions.

Part c· 4 steps
$\frac{1}{2}$

Find a common denominator for $\frac{1}{3}$ and $\frac{1}{6}$ .

Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 6.

Add the fractions.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.

Part d· 3 steps
$\frac{3}{8}$

Find a common denominator for $\frac{1}{8}$ and $\frac{1}{4}$ .

Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8.

Add the fractions.

Part e· 3 steps
$\frac{9}{20}$

Find a common denominator for $\frac{1}{5}$ and $\frac{1}{4}$ .

Convert both fractions to equivalent fractions with a denominator of 20.

Add the fractions.

Part f· 3 steps
$\frac{5}{6}$

Find a common denominator for $\frac{1}{2}$ and $\frac{1}{3}$ .

Convert both fractions to equivalent fractions with a denominator of 6.

Add the fractions.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Calculate and simplify if necessary. Example: 1/2 + 1/3 = 5/6. Where does the 6 come from?

Answers

Step-by-step solution

Part a· 3 steps

Find a common denominator for 14\frac{1}{4}41​ and 12\frac{1}{2}21​.

Convert 12\frac{1}{2}21​ to an equivalent fraction with a denominator of 4.

Add the fractions.

Part b· 3 steps310\frac{3}{10}103​

Find a common denominator for 15\frac{1}{5}51​ and 110\frac{1}{10}101​.

Convert 15\frac{1}{5}51​ to an equivalent fraction with a denominator of 10.

Add the fractions.

Part c· 4 steps12\frac{1}{2}21​

Find a common denominator for 13\frac{1}{3}31​ and 16\frac{1}{6}61​.

Convert 13\frac{1}{3}31​ to an equivalent fraction with a denominator of 6.

Add the fractions.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.

Part d· 3 steps38\frac{3}{8}83​

Find a common denominator for 18\frac{1}{8}81​ and 14\frac{1}{4}41​.

Convert 14\frac{1}{4}41​ to an equivalent fraction with a denominator of 8.

Add the fractions.

Part e· 3 steps920\frac{9}{20}209​

Find a common denominator for 15\frac{1}{5}51​ and 14\frac{1}{4}41​.

Convert both fractions to equivalent fractions with a denominator of 20.

Add the fractions.

Part f· 3 steps56\frac{5}{6}65​

Find a common denominator for 12\frac{1}{2}21​ and 13\frac{1}{3}31​.

Convert both fractions to equivalent fractions with a denominator of 6.

Add the fractions.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Find a common denominator for $\frac{1}{4}$ and $\frac{1}{2}$ .

Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 4.

Part b· 3 steps
$\frac{3}{10}$

Find a common denominator for $\frac{1}{5}$ and $\frac{1}{10}$ .

Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 10.

Part c· 4 steps
$\frac{1}{2}$

Find a common denominator for $\frac{1}{3}$ and $\frac{1}{6}$ .

Convert $\frac{1}{3}$ to an equivalent fraction with a denominator of 6.

Part d· 3 steps
$\frac{3}{8}$

Find a common denominator for $\frac{1}{8}$ and $\frac{1}{4}$ .

Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8.

Part e· 3 steps
$\frac{9}{20}$

Find a common denominator for $\frac{1}{5}$ and $\frac{1}{4}$ .

Part f· 3 steps
$\frac{5}{6}$

Find a common denominator for $\frac{1}{2}$ and $\frac{1}{3}$ .