Solve the Expression: 5 - 2 × 3/4 Using Order of Operations

Q: Why can't I just work from left to right like in reading?

Mathematics has its own reading order! The order of operations (PEMDAS) ensures everyone gets the same answer. Multiplication always comes before subtraction, no matter where it appears in the expression.

Q: How do I multiply a whole number by a fraction?

Multiply the whole number by the numerator: $ 2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{6}{4} $. Then simplify by dividing both numerator and denominator by their greatest common factor.

Q: What's the easiest way to subtract fractions from whole numbers?

Convert everything to the same form! Either convert $ 5 $ to $ \frac{10}{2} $ and subtract $ \frac{3}{2} $, or convert $ \frac{3}{2} $ to $ 1\frac{1}{2} $ and subtract from $ 5 $.

Q: Should my final answer be an improper fraction or mixed number?

Since the answer choices are mixed numbers, convert your improper fraction to a mixed number. $ \frac{7}{2} = 3\frac{1}{2} $ because 7 ÷ 2 = 3 remainder 1.

Q: How can I check if 3½ is really correct?

Substitute back: $ 5 - 2 \times \frac{3}{4} = 5 - \frac{6}{4} = 5 - 1\frac{1}{2} = 3\frac{1}{2} $. You can also convert to decimals: $ 5 - 2 \times 0.75 = 5 - 1.5 = 3.5 = 3\frac{1}{2} $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 First, multiply the top number, or numerator, and keep the botto m number, called the denominato r, the same.

00:15 Next, use the distribution law. Break down 4 into two times two.

00:23 Simplify as much as you can. You're doing great!

00:28 Now, change the fraction into a whole number with a remainder.

00:33 And that's how we find the solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$5-2\times\frac{3}{4}=$

2

Step-by-step solution

We add the 2 to the numerator of the fraction in the multiplication exercise, and the 4 in the denominator of the fraction we break it down into a smaller multiplication exercise:

$5-\frac{2\times3}{2\times2}=$

We simplify the 2 in the numerator and denominator:

$5-\frac{3}{2}=$

We convert the simple fraction into a mixed fraction:

$5-1\frac{1}{2}=3\frac{1}{2}$

3

Final Answer

$3\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS - multiplication before subtraction always
Technique: Calculate $2\times\frac{3}{4} = \frac{6}{4} = \frac{3}{2}$ first
Check: Verify $5 - 1\frac{1}{2} = 3\frac{1}{2}$ using mixed number subtraction ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't calculate 5 - 2 = 3 first, then multiply by 3/4 = 9/4! This ignores PEMDAS and gives the wrong answer. Always do multiplication before subtraction, so calculate 2 × 3/4 first, then subtract from 5.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why can't I just work from left to right like in reading?

+

Mathematics has its own reading order! The order of operations (PEMDAS) ensures everyone gets the same answer. Multiplication always comes before subtraction, no matter where it appears in the expression.

How do I multiply a whole number by a fraction?

+

Multiply the whole number by the numerator: $2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{6}{4}$ . Then simplify by dividing both numerator and denominator by their greatest common factor.

What's the easiest way to subtract fractions from whole numbers?

+

Convert everything to the same form! Either convert $5$ to $\frac{10}{2}$ and subtract $\frac{3}{2}$ , or convert $\frac{3}{2}$ to $1\frac{1}{2}$ and subtract from $5$ .

Should my final answer be an improper fraction or mixed number?

+

Since the answer choices are mixed numbers, convert your improper fraction to a mixed number. $\frac{7}{2} = 3\frac{1}{2}$ because 7 ÷ 2 = 3 remainder 1.

How can I check if 3½ is really correct?

+

Substitute back: $5 - 2 \times \frac{3}{4} = 5 - \frac{6}{4} = 5 - 1\frac{1}{2} = 3\frac{1}{2}$ . You can also convert to decimals: $5 - 2 \times 0.75 = 5 - 1.5 = 3.5 = 3\frac{1}{2}$ ✓

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Solve the Expression: 5 - 2 × 3/4 Using Order of Operations

Order of Operations with Mixed Numbers

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