Evaluate The Expression:$\[\frac{1}{8} + \frac{3}{4}\\]

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the expression $\frac{1}{8} + \frac{3}{4}$ and provide a step-by-step solution to simplify the expression.

Understanding the Expression

The given expression is a sum of two fractions: $\frac{1}{8}$ and $\frac{3}{4}$. To evaluate this expression, we need to find a common denominator for the two fractions. The common denominator is the least common multiple (LCM) of the denominators of the two fractions.

Finding the Common Denominator

To find the common denominator, we need to find the LCM of 8 and 4. The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 520, 528, 536, 544, 552, 560, 568, 576, 584, 592, 600, 608, 616, 624, 632, 640, 648, 656, 664, 672, 680, 688, 696, 704, 712, 720, 728, 736, 744, 752, 760, 768, 776, 784, 792, 800, 808, 816, 824, 832, 840, 848, 856, 864, 872, 880, 888, 896, 904, 912, 920, 928, 936, 944, 952, 960, 968, 976, 984, 992, 1000, 1008, 1016, 1024, 1032, 1040, 1048, 1056, 1064, 1072, 1080, 1088, 1096, 1104, 1112, 1120, 1128, 1136, 1144, 1152, 1160, 1168, 1176, 1184, 1192, 1200, 1208, 1216, 1224, 1232, 1240, 1248, 1256, 1264, 1272, 1280, 1288, 1296, 1304, 1312, 1320, 1328, 1336, 1344, 1352, 1360, 1368, 1376, 1384, 1392, 1400, 1408, 1416, 1424, 1432, 1440, 1448, 1456, 1464, 1472, 1480, 1488, 1496, 1504, 1512, 1520, 1528, 1536, 1544, 1552, 1560, 1568, 1576, 1584, 1592, 1600, 1608, 1616, 1624, 1632, 1640, 1648, 1656, 1664, 1672, 1680, 1688, 1696, 1704, 1712, 1720, 1728, 1736, 1744, 1752, 1760, 1768, 1776, 1784, 1792, 1800, 1808, 1816, 1824, 1832, 1840, 1848, 1856, 1864, 1872, 1880, 1888, 1896, 1904, 1912, 1920, 1928, 1936, 1944, 1952, 1960, 1968, 1976, 1984, 1992, 2000, 2008, 2016, 2024, 2032, 2040, 2048, 2056, 2064, 2072, 2080, 2088, 2096, 2104, 2112, 2120, 2128, 2136, 2144, 2152, 2160, 2168, 2176, 2184, 2192, 2200, 2208, 2216, 2224, 2232, 2240, 2248, 2256, 2264, 2272, 2280, 2288, 2296, 2304, 2312, 2320, 2328, 2336, 2344, 2352, 2360, 2368, 2376, 2384, 2392, 2400, 2408, 2416, 2424, 2432, 2440, 2448, 2456, 2464, 2472, 2480, 2488, 2496, 2504, 2512, 2520, 2528, 2536, 2544, 2552, 2560, 2568, 2576, 2584, 2592, 2600, 2608, 2616, 2624, 2632, 2640, 2648, 2656, 2664, 2672, 2680, 2688, 2696, 2704, 2712, 2720, 2728, 2736, 2744, 2752, 2760, 2768, 2776, 2784, 2792, 2800, 2808, 2816, 2824, 2832, 2840, 2848, 2856, 2864, 2872, 2880, 2888, 2896, 2904, 2912, 2920, 2928, 2936, 2944, 2952, 2960, 2968, 2976, 2984, 2992, 3000, 3008, 3016, 3024, 3032, 3040, 3048, 3056, 3064, 3072, 3080, 3088, 3096, 3104, 3112, 3120, 3128, 3136, 3144, 3152, 3160, 3168, 3176, 3184, 3192, 3200, 3208, 3216, 3224, 3232, 3240, 3248, 3256, 3264, 3272, 3280, 3288, 3296, 3304, 3312, 3320, 3328, 3336, 3344, 3352, 3360, 3368, 3376, 3384, 3392, 3400, 3408, 3416, 3424, 3432, 3440, 3448, 3456, 3464, 3472, 3480, 3488, 3496, 3504, 3512, 3520, 3528, 3536, 3544, 3552, 3560, 3568, 3576, 3584, 3592, 3600, 3608, 3616, 3624, 3632, 3640, 3648, 3656, 3664, 3672, 3680, 3688, 3696, 3704, 3712, 3720, 3728, 3736, 3744, 3752, 3760, 3768, 3776, 3784, 3792, 3800, 3808, 3816, 3824, 3832, 3840, 3848, 3856, 3864, 3872, 3880, 3888, 3896, 3904, 3912, 3920, 3928, 3936, 3944, 3952, 3960,

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the expression $\frac{1}{8} + \frac{3}{4}$ and provide a step-by-step solution to simplify the expression.

Understanding the Expression

The given expression is a sum of two fractions: $\frac{1}{8}$ and $\frac{3}{4}$. To evaluate this expression, we need to find a common denominator for the two fractions. The common denominator is the least common multiple (LCM) of the denominators of the two fractions.

Finding the Common Denominator

To find the common denominator, we need to find the LCM of 8 and 4. The LCM of 8 and 4 is 8.

Evaluating the Expression

Now that we have found the common denominator, we can evaluate the expression by adding the two fractions.

$\frac{1}{8} + \frac{3}{4} = \frac{1}{8} + \frac{6}{8}$

Simplifying the Expression

Now that we have added the two fractions, we can simplify the expression by combining the numerators.

$\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$

Conclusion

In conclusion, the expression $\frac{1}{8} + \frac{3}{4}$ can be simplified to $\frac{7}{8}$.

Q&A

Q: What is the common denominator of $\frac{1}{8}$ and $\frac{3}{4}$?

A: The common denominator of $\frac{1}{8}$ and $\frac{3}{4}$ is 8.

Q: How do you evaluate the expression $\frac{1}{8} + \frac{3}{4}$?

A: To evaluate the expression $\frac{1}{8} + \frac{3}{4}$, you need to find a common denominator for the two fractions. The common denominator is the least common multiple (LCM) of the denominators of the two fractions. Once you have found the common denominator, you can add the two fractions.

Q: What is the simplified form of the expression $\frac{1}{8} + \frac{3}{4}$?

A: The simplified form of the expression $\frac{1}{8} + \frac{3}{4}$ is $\frac{7}{8}$.

Q: Why do you need to find a common denominator when adding fractions?

A: You need to find a common denominator when adding fractions because the denominators of the fractions must be the same in order to add them.

Q: What is the least common multiple (LCM) of 8 and 4?

A: The least common multiple (LCM) of 8 and 4 is 8.

Q: How do you add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator for the two fractions. Once you have found the common denominator, you can add the two fractions.

Q: What is the final answer to the expression $\frac{1}{8} + \frac{3}{4}$?

A: The final answer to the expression $\frac{1}{8} + \frac{3}{4}$ is $\frac{7}{8}$.

Additional Resources

• Mathway: A math problem solver that can help you solve math problems and evaluate expressions.
• Khan Academy: A free online learning platform that provides video lessons and practice exercises on various math topics, including fractions and expressions.
• Wolfram Alpha: A computational knowledge engine that can help you solve math problems and evaluate expressions.

Conclusion

In conclusion, evaluating expressions is a fundamental concept in mathematics that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we have evaluated the expression $\frac{1}{8} + \frac{3}{4}$ and provided a step-by-step solution to simplify the expression. We have also answered some common questions related to evaluating expressions and provided additional resources for further learning.