Math Problem Statement

7 number question

Simplify: (4/5) * 20 - 1/2 + 1/4

Solution

I see you uploaded an image containing mathematical problems. The seventh question in the image seems to involve solving a mathematical expression for simplification. Let me transcribe it:

7. Simplify:

45×2012+14\frac{4}{5} \times 20 - \frac{1}{2} + \frac{1}{4}

I'll simplify this for you step by step:

Step 1: Solve the multiplication

45×20=4×205=805=16\frac{4}{5} \times 20 = \frac{4 \times 20}{5} = \frac{80}{5} = 16

Step 2: Substitute into the expression

1612+1416 - \frac{1}{2} + \frac{1}{4}

Step 3: Get a common denominator for the fractions

The least common denominator (LCD) between 2 and 4 is 4. So, we rewrite the fractions:

12=24\frac{1}{2} = \frac{2}{4}

Now the expression becomes:

1624+1416 - \frac{2}{4} + \frac{1}{4}

Step 4: Combine the fractions

2+14=14\frac{-2 + 1}{4} = \frac{-1}{4}

Step 5: Final calculation

1614=64414=63416 - \frac{1}{4} = \frac{64}{4} - \frac{1}{4} = \frac{63}{4}

So the final answer is:

634\boxed{\frac{63}{4}}

Would you like more details or have any questions?

Here are five related questions:

  1. How do you convert mixed fractions into improper fractions for simplification?
  2. How do you determine the least common denominator when working with fractions?
  3. Can you explain how to handle subtraction between mixed numbers?
  4. How would you simplify an expression involving both multiplication and division of fractions?
  5. What are some common mistakes when adding and subtracting fractions?

Tip: Always simplify your fractions as early as possible in a problem to make calculations easier!

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Math Problem Analysis

Mathematical Concepts

Fraction Operations
Multiplication
Subtraction
Addition
Simplification

Formulas

Multiplication of fractions: (a/b) * c = (a * c) / b
Addition and subtraction of fractions: a/b + c/d = (ad + bc) / bd

Theorems

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Suitable Grade Level

Grade 6-8