First estimate each answer and then find the exact answer using the column method: a) \( 176249+0+890385 \) c) \( 32046290+43748341 \) e) \( 117454454+11909909+190231044 \) b) \( (340357+119238)+0 \) f) \( 230394506+116460079+56043921 \) What do you notice when you add 0 to a number?

Sure, let's tackle each addition problem step by step. We'll start by estimating the sums and then calculate the exact answers using the column method. Finally, we'll address what happens when you add 0 to a number. --- ### a) \( 176,249 + 0 + 890,385 \) **Estimation:** - \( 176,000 + 0 + 890,000 = 1,066,000 \) **Exact Calculation (Column Method):** ``` 176,249 + 0 + 890,385 ----------- 1,066,634 ``` **Answer:** \( 1,066,634 \) --- ### c) \( 32,046,290 + 43,748,341 \) **Estimation:** - \( 32,000,000 + 44,000,000 = 76,000,000 \) **Exact Calculation (Column Method):** ``` 32,046,290 +43,748,341 ------------ 75,794,631 ``` **Answer:** \( 75,794,631 \) --- ### e) \( 117,454,454 + 11,909,909 + 190,231,044 \) **Estimation:** - \( 117,000,000 + 12,000,000 + 190,000,000 = 319,000,000 \) **Exact Calculation (Column Method):** 1. **First Addition:** ``` 117,454,454 + 11,909,909 ------------ 129,364,363 ``` 2. **Second Addition:** ``` 129,364,363 +190,231,044 ------------ 319,595,407 ``` **Answer:** \( 319,595,407 \) --- ### b) \( (340,357 + 119,238) + 0 \) **Estimation:** - \( 340,000 + 120,000 + 0 = 460,000 \) **Exact Calculation (Column Method):** 1. **First Addition:** ``` 340,357 + 119,238 ---------- 459,595 ``` 2. **Adding Zero:** ``` 459,595 + 0 ---------- 459,595 ``` **Answer:** \( 459,595 \) --- ### f) \( 230,394,506 + 116,460,079 + 56,043,921 \) **Estimation:** - \( 230,000,000 + 116,000,000 + 56,000,000 = 402,000,000 \) **Exact Calculation (Column Method):** 1. **First Addition:** ``` 230,394,506 +116,460,079 ------------ 346,854,585 ``` 2. **Second Addition:** ``` 346,854,585 + 56,043,921 ------------ 402,898,506 ``` **Answer:** \( 402,898,506 \) --- ### **What do you notice when you add 0 to a number?** When you add **0** to any number, the value of the original number **remains unchanged**. This is because **0** is known as the **additive identity** in mathematics. In simple terms: \[ \text{Number} + 0 = \text{Number} \] This property holds true for all real numbers, making 0 a unique and essential element in arithmetic operations. ---