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Texas Grab-and-Go Substitute Packet

Fractions and Decimals in Everyday Problems

Grade: 5 Subject: Mathematics Time: ~45 min core + ~15 min extension Work mode: Independent · pencil + packet Math

Start Here

This is a paper math packet about fractions and decimals. Work by yourself with a pencil. A calculator is not required, but a basic calculator is allowed if you have one. Show your work — write the steps you used, not just a final number. Everything you need is printed right here, including a worked example. If a question is hard, skip it, keep going, and come back. Box your final answers.

Start Warm-Up 5 min

Bring back what you already know about decimals and fractions.

1Compare two decimals. Write <, >, or = between these two numbers, then tell in one sentence how you knew: 0.7 ☐ 0.68.

2Name the fraction. The bar below is cut into equal parts, and some parts are shaded. Write the fraction of the whole bar that is shaded.

A bar split into 5 equal parts with 3 parts shaded A rectangle divided by vertical lines into five equal parts. Three of the five parts are filled with a diagonal-line pattern; the other two parts are white.
Figure 1. A bar cut into equal parts, with some parts shaded.

Build Study the Math 5–10 min

What you need to know

Comparing decimals (to thousandths). Line up numbers by place value, not by how many digits they have. Compare left to right: tenths, then hundredths, then thousandths. It helps to add zeros so both numbers have the same number of decimal places. Example: to compare 0.7 and 0.68, write 0.7 as 0.70. Now 0.70 vs 0.68 → 7 tenths beats 6 tenths, so 0.70 > 0.68.

Adding & subtracting fractions with unlike denominators. You can only add or subtract fractions when the parts are the same size — that means the same denominator (the bottom number). Steps:

  1. Find a common denominator (a number both bottoms divide into). Multiplying the two bottoms always works.
  2. Rename each fraction as an equal fraction with that common bottom (multiply the top and bottom by the same number).
  3. Add or subtract only the tops (numerators). Keep the common bottom.

1/2 + 1/4  →  2/4 + 1/4 = 3/4

Connecting a fraction to its decimal. A fraction is a division: the top divided by the bottom. If you can rename a fraction with a bottom of 10, 100, or 1000, you can read the decimal straight off. Examples: 1/2 = 5/10 = 0.5, and 3/4 = 75/100 = 0.75.

Watch out: 1/2 is 0.5, not 0.2. And when comparing decimals, 0.7 is bigger than 0.68 even though 0.68 has more digits.

Worked Example — adding fractions with unlike denominators

Add 1/2 + 1/3. The bottoms are different (2 and 3), so the parts are different sizes. First find a common bottom.

Step 1 — common denominator: 2 × 3 = 6. Sixths work for both.

Step 2 — rename each fraction: 1/2 = 3/6 (multiply top and bottom by 3), and 1/3 = 2/6 (multiply top and bottom by 2).

Step 3 — add the tops: 3/6 + 2/6 = 5/6. The picture below shows why: three sixths plus two sixths fills five of the six equal parts.

Area model showing one half plus one third equals five sixths Three same-size bars stacked. The top bar is split into two equal parts with one half shaded in a diagonal pattern, labeled one half equals three sixths. The middle bar is split into three equal parts with one third shaded in a dotted pattern, labeled one third equals two sixths. The bottom bar is split into six equal parts; five of the six parts are shaded, three in the diagonal pattern and two in the dotted pattern, labeled five sixths. A number line below the bars runs from 0 to 1 in sixths, with an arrow ending at five sixths. 1/2 = 3/6 1/3 = 2/6 = 5/6 0 1/6 2/6 3/6 4/6 5/6 1 start at 0, land on 5/6
Figure 2. An area model and number line for 1/2 + 1/3. Renaming both fractions into sixths (3/6 and 2/6) makes the parts the same size, so they add to 5/6. The diagonal pattern shows the half; the dotted pattern shows the third. Drawn in black so it reads clearly in grayscale.

3Using the worked example as your guide, add 1/2 + 1/4. Rename to a common denominator first, then add the tops. Show each step.

Apply Use What You Know 20–25 min

Show the steps you use in every item. A basic calculator is allowed.

4Recipe (adding fractions). A snack recipe uses 1/2 cup of raisins and 1/3 cup of almonds. How many cups of raisins and almonds are there in all? Find a common denominator, rename, and add. Show your steps.

5Money (decimals). Maya buys a notebook for $3.45 and a pen for $1.60.

5a. How much does she spend in all? Line up the decimal points and add.

5b. She pays with a $10.00 bill. How much change does she get back? Show your subtraction.

6Find and fix the error. A student added two fractions this way. Find the mistake, explain it, and give the correct answer in the box.

Student's work:

1/4 + 1/2 = (1 + 1) / (4 + 2) = 2/6

What is wrong, and what is the correct sum?

7Which operation? (multi-step). A water bottle holds 2 liters. José drinks 3/4 liter in the morning and 1/2 liter at lunch.

7a. How much has José drunk in all? Decide the operation, then find a common denominator and add. Show your steps.

7b. One tip for choosing the operation: "in all" usually means add; "how much is left" usually means subtract. In one sentence, tell which words in part 7a told you to add.

Explain Justify Your Thinking 5–10 min

Question 8. In problem 6, a student wrote 1/4 + 1/2 = 2/6. Explain why you cannot just add the tops and add the bottoms. Use the frame below: write your Answer, the Numbers you used, and Why your way is correct.

Sentence starters you may use: "The correct sum is ___ because…" · "First I found a common denominator by…" · "I renamed 1/4 as ___ and 1/2 as ___…" · "You cannot add the bottoms because the parts must be…"

Answer (the correct sum)
Numbers I used
Why my way is correct

Close ACE Wrap-Up 5 min

Articulate

In your own words, explain what a common denominator is and why you need one to add fractions.

Connect

Point to one item in this packet where you found a common denominator. Give its number.

Extend

Write a fraction and its matching decimal that was not in this packet (for example, a fraction equal to a number of tenths or hundredths).

Continue Early Finisher optional · ~15 min

If you finish early (no new materials needed):

Draw your own model. On the back of this page, add 1/3 + 1/6. First find a common denominator, then draw an area model or a number line like Figure 2 to show the sum. Label the parts, and write the final answer as a fraction. If you can, also write it as a decimal.

Turn in: Hand in this whole packet with your name, class period, and date filled in. Make sure questions 1–8 and the ACE box are answered with your work shown. The early-finisher challenge is optional, but turn it in too if you did it.
G05_MATH_FractionsDecimals_01 — Fractions and Decimals in Everyday Problems Student Packet