Q. \(\frac{2}{3} + \frac{2}{3} =\).

Q: What is the sum of two thirds plus two thirds?

\frac{2}{3} + \frac{2}{3} = \frac{4}{3} , which is an improper fraction equal to the mixed number 1\frac{1}{3}.

Q: How do you add fractions with the same denominator?

Keep the denominator and add numerators: \frac{a}{d} + \frac{b}{d} = \frac{a+b}{d} . Here \frac{2}{3}+\frac{2}{3}=\frac{4}{3}.

Q: How do you convert \frac{4}{3} to a mixed number?

Divide: 4\div3=1 remainder 1. So \frac{4}{3}=1\frac{1}{3} (one whole and one third).

Q: How would you show \frac{2}{3}+\frac{2}{3} on a number line?

Start at 0, move right \frac{2}{3} then another \frac{2}{3} ; you land at \frac{4}{3} , which is one whole and one third past 0.

Q: What's a common mistake when adding fractions like these?

Adding denominators: incorrect \frac{2+2}{3+3}=\frac{4}{6} . Always find a common denominator (here already 3) and add numerators.

Answer

\[\frac{2}{3}+\frac{2}{3}=\frac{4}{3}=1\frac{1}{3}\] Add numerators: 2 + 2 = 4, denominator remains 3.

Detailed Explanation

Problem

Add: two thirds plus two thirds.

Step-by-step solution

Write the problem using fractional notation.

\( \tfrac{2}{3} + \tfrac{2}{3} \)
Observe the denominators. Both fractions have the same denominator, 3, so you can add the numerators directly while keeping the denominator the same.

Keep the denominator 3 and add the numerators 2 and 2.

\( \tfrac{2}{3} + \tfrac{2}{3} = \tfrac{2 + 2}{3} \)
Compute the sum of the numerators.

\( \tfrac{2 + 2}{3} = \tfrac{4}{3} \)
Convert the improper fraction to a mixed number by dividing the numerator by the denominator. Divide 4 by 3 to find how many whole units and what remainder remains.

4 divided by 3 is 1 with remainder 1, so

\( \tfrac{4}{3} = 1\ \tfrac{1}{3} \)
Optionally, express the mixed number as a decimal. \(1\ \tfrac{1}{3} = 1.333\ldots\)

Final answer

\( \tfrac{2}{3} + \tfrac{2}{3} = \tfrac{4}{3} = 1\ \tfrac{1}{3} \)

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FAQs

What is the sum of two thirds plus two thirds?

\( \frac{2}{3} + \frac{2}{3} = \frac{4}{3} \), which is an improper fraction equal to the mixed number \(1\frac{1}{3}\).

How do you add fractions with the same denominator?

Keep the denominator and add numerators: \( \frac{a}{d} + \frac{b}{d} = \frac{a+b}{d} \). Here \( \frac{2}{3}+\frac{2}{3}=\frac{4}{3}\).

Why is \( \frac{4}{3} \) called an improper fraction?

Because the numerator (4) is larger than the denominator (3). Improper fractions represent quantities greater than or equal to 1.

How do you convert \( \frac{4}{3} \) to a mixed number?

Divide: \(4\div3=1\) remainder \(1\). So \( \frac{4}{3}=1\frac{1}{3}\) (one whole and one third).

How would you show \( \frac{2}{3}+\frac{2}{3} \) on a number line?

Start at 0, move right \( \frac{2}{3} \) then another \( \frac{2}{3} \); you land at \( \frac{4}{3} \), which is one whole and one third past 0.

What's the decimal and percent form of the sum?

What's a common mistake when adding fractions like these?

Adding denominators: incorrect \( \frac{2+2}{3+3}=\frac{4}{6} \). Always find a common denominator (here already 3) and add numerators.

How would you add fractions with different denominators instead?

Find a common denominator (least common multiple), convert each fraction, then add numerators. Example: \( \frac{2}{3}+\frac{1}{4}=\frac{8}{12}+\frac{3}{12}=\frac{11}{12}\).

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