Question

Use your fraction pieces or another method to help fill in each blank. \(\frac{1}{4}+\quad=1\)

Short answer

The missing fraction is \(\frac{3}{4}\).

Step-by-step solution

Understand the Problem

The task is to find a fraction that, when added to \(\frac{1}{4}\), results in 1. In other words, solve for the unknown fraction \(\frac{1}{4} + \text{?} = 1\).

Convert 1 to Fraction Form

Rewrite 1 as a fraction with the same denominator as \(\frac{1}{4}\). Since \(\frac{1}{4}\) has a denominator of 4, we write 1 as \(\frac{4}{4}\). Now the equation becomes \(\frac{1}{4} + \text{?} = \frac{4}{4}\).

Subtract \(\frac{1}{4}\) from Both Sides

To isolate the unknown fraction, subtract \(\frac{1}{4}\) from both sides of the equation: \(\frac{4}{4} - \frac{1}{4} = \text{?}\).

Perform the Subtraction

Subtract the fractions: \(\frac{4}{4} - \frac{1}{4} = \frac{4-1}{4} = \frac{3}{4}\). This means that \(\text{?} = \frac{3}{4}\).

Verify the Solution

Add \(\frac{1}{4}\) and \(\frac{3}{4}\) to check the result: \(\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1\). The solution is correct.

Key concepts

Fraction Addition

Adding fractions might seem complex at first, but it's simple once you understand the steps. When adding fractions, it's crucial to have a common denominator. This makes the process straightforward and equivalent. For example, adding \(\frac{1}{4} + \frac{3}{4}\) is easy because both fractions already have the same denominator, which is 4. You just add the numerators: \(\frac{1+3}{4} = \frac{4}{4} = 1\). Here, the denominator stays the same, and you only change the numerator. Just remember:

• Find a common denominator if it's not given.
• Add only the numerators.
• Keep the denominator the same.

Adding fractions is simple with these steps in mind.

Equivalent Fractions

Understanding equivalent fractions is essential when working with fractions. Equivalent fractions are different fractions that represent the same value. For instance, \(\frac{2}{4}\) is equivalent to \(\frac{1}{2}\) because they both equal 0.5. You can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number. Here are some tips:

• Multiplication Method: Multiply both the numerator and the denominator by the same number. For example, \(\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}\).
• Division Method: Divide both the numerator and the denominator by the same number. For example, \(\frac{4}{8} \div \ 4 = \frac{1}{2}\).

This can help you simplify fractions or find a common denominator.

Solving Equations

Solving equations with fractions involves isolating the variable. This often includes converting one side to match the other, as in the original exercise where we rewrote 1 as \(\frac{4}{4}\). Then you subtract the given fraction from both sides to isolate the unknown fraction. Breaking it down:

• Rewriting: Adjust the fractions to have common denominators.
• Isolation: Subtract or add fractions to isolate the variable.
• Simplify: Always simplify your final answer if possible.

For example, in the equation \(\frac{1}{4} + \text{?} = 1\), we rewrote 1 as \(\frac{4}{4}\) to find the solution. This makes it easier to subtract and solve for the unknown.